It is hard to impossible to help you, you are so vague in your description ("a project", "a class", desktop for which system?).

Let see some error messages, at least.
Class Maxim is missing. We don't know what this class is. Is it from some library, or are you missing a file from the project?
"needs to be in a folder called": a sketch has a name. This name is used to name the main .pde file in the sketch, which must be in the sketchbook, in a folder of same name:
sketchbook
 \
  - SomeName
      \
       - SomeName.pde
The sketchbook is the place where all your sketches (and libraries, tools, modes...) are located.
It is a folder distinct from the installation folder, which must remain unchanged.
You can find its location in the Preferences dialog of the PDE.

The last message can be triggered if you have a class named ProjectQuads in a .pde file of same name: it confuses Processing, which creates behind a scene its own class with the name of the sketch, so it finds two identical classes and doesn't know which one to choose. See the Common issues with sketch names article.

Note: these are not really programming questions (about some code), so I moved the topic. See also https://forum.processing.org/topic/where-to-place-threads-and-other-forum-practices
I hope you will enjoy your Processing trip, once these initial hurdles are overcome.

Thank you. That helped alot, but it did not solve my problem.

So - My file structure is as follows;

Documents\Processing\ProjectedQuads\ProjectedQuads.pde

When I run ProjectedQuads.pde it tells me "The nested type ProjectedQuads cannot hide an enclosing type". After looking around I've tried some things.

1) I took the ProjectedQuads.pde and placed it in the parent folder. But then when I open it processing tells me it needs to be in a folder named so. So I let it do that...

2) Someone suggested a class was declared twice to someone with the same problem - to remove the contents and delete the second decleration, so I tried that with the following code and came across bigger issues, so I don't think that is the fix

1. class ProjectedQuads {
     private ArrayList quads;
     private boolean debugMode = true;
     private int selectedQuad = 0;
     private int selectedPoint = 0; 
     private float numSubdivisions = 5;
     PFont debugFont;
    
     public ProjectedQuads() {
       quads = new ArrayList();
       debugFont = createFont("Arial", 64);
     }
    
     public boolean getDebugMode() {
       return debugMode;
     }
    
     public void setDebugMode(boolean debugMode) {
       this.debugMode = debugMode;
     }
    
     public void setNumQuads(int num) {
       while(quads.size() > num) {
         quads.remove(quads.size()-1);
       }
       while(quads.size() < num) {
         quads.add(new Quad());
       }
       selectedQuad = quads.size()-1;
     }
    
     public int getNumQuads() {
       return quads.size();
     }
    
     public Quad getQuad(int i) {
       return (Quad)quads.get(i);
     }
    
     public void load(String configFile) {
       String[] data = loadStrings(configFile);
       if (data == null) {
         return;
       }
       setNumQuads(data.length);
       for(int i=0; i<data.length; i++) {
         PVector[] points = ((Quad)quads.get(i)).getPoints();
         String[] lineArr = data[i].split(" ");
         for(int j=0; j<4; j++) {
           points[j].x = parseFloat(lineArr[j*2]);
           points[j].y = parseFloat(lineArr[j*2+1]);
         }   
       }
       println("ProjectedQuads loaded from: " + configFile);
     }
    
     public void save(String configFile) {
       String data = "";
       for(int i=0; i<quads.size(); i++) {
         PVector[] points = ((Quad)quads.get(i)).getPoints();
         for(int j=0; j<4; j++) {
           data += points[j].x + " " + points[j].y;
           if (j < 3) data += " ";
         }
         if (i < quads.size()-1) data += "\n";
       }
       saveStrings(configFile, data.split("\n"));
       println("ProjectedQuads saved to: " + configFile);
     }
        
    
     //draw all the quads
     public void draw() {   
       if (debugMode) {
         textFont(debugFont);
       }
      
       for(int i=0; i<quads.size(); i++) {   
         if (debugMode) {
           if (i == selectedQuad) {
             stroke(255, 0, 0, 255);
           }
           else {
             stroke(255, 0, 0, 50);
           }
         }
         else {
           noStroke();
         }   
         beginShape(QUADS);  
         Quad q = (Quad)quads.get(i);
         texture(q.getTexture());
        
         for(int x=0; x<numSubdivisions; x++) {
           for(int y=0; y<numSubdivisions; y++) {
             calcVertex(q, x/numSubdivisions, y/numSubdivisions);
             calcVertex(q, (x+1)/numSubdivisions, y/numSubdivisions);
             calcVertex(q, (x+1)/numSubdivisions, (y+1)/numSubdivisions);
             calcVertex(q, x/numSubdivisions, (y+1)/numSubdivisions);
           }
         }
         endShape();
         if (debugMode) {
           PVector center = q.getCenterPoint();
          
           fill(0, 0, 0); 
           text(""+i, center.x-22, center.y+22);          
          
           if (i == selectedQuad) {
               fill(0, 255, 0); 
           }
           else {
               fill(255, 0, 0);
           }
          
           text(""+i, center.x-20, center.y+20);   
         }
       }
      
       if (debugMode) {
         drawAnchors();
       }
     } 
    
     //calculates vertex for sub quads
     public void calcVertex(Quad q, float sx, float sy) {
       PVector[] points = q.getPoints();
       float tx = points[0].x + (points[1].x - points[0].x)*sx;
       float ty = points[0].y + (points[1].y - points[0].y)*sx;       
       float bx = points[3].x + (points[2].x - points[3].x)*sx;
       float by = points[3].y + (points[2].y - points[3].y)*sx;  
       float gw = q.getTexture().width;
       float gh = q.getTexture().height;   
    
       if(q.isMirrored()) {
         vertex(tx + (bx - tx) * sy, ty + (by - ty) * sy, gw-sx*gw, sy*gh);
       }
       else {
         vertex(tx + (bx - tx) * sy, ty + (by - ty) * sy, sx*gw, sy*gh);
       } 
     }
    
     public void drawAnchors() {
       stroke(255, 0, 0);
       rectMode(CENTER);  
       if (selectedQuad > -1) {   
         Quad q = (Quad)quads.get(selectedQuad);
        
         for(int i=0; i<4; i++) { 
           if (i == selectedPoint) {
             fill(0, 255, 0);
           }
           else {
             fill(255, 0, 0);
           }
           rect(q.getPoints()[i].x, q.getPoints()[i].y, 10, 10);
         }
       }
     }
    
    
     public void keyPressed() {
       if (selectedQuad > -1 && selectedPoint > -1) {
         PVector[] points = ((Quad)quads.get(selectedQuad)).getPoints();
         switch(keyCode) {
         case LEFT:
           points[selectedPoint].x -= 1;
           break;
         case RIGHT:
           points[selectedPoint].x += 1;
           break;
         case UP:
           points[selectedPoint].y -= 1;
           break;
         case DOWN:
           points[selectedPoint].y += 1;
           break;     
         }
       }
      
       if (key == '1') {
         selectedPoint = 0;
       }
       if (key == '2') {
         selectedPoint = 1;
       }
       if (key == '3') {
         selectedPoint = 2;
       }
       if (key == '4') {
         selectedPoint = 3;
       }
       if (key == '<') {
         selectedQuad = (selectedQuad - 1 + quads.size()) % quads.size();
       }
       if (key == '>') {
         selectedQuad = (selectedQuad + 1) % quads.size();
       }
      
       //Shift + 's' to avoid accidental saving
       if (key == 'S') {
         projectedQuads.save(configFile);
       }
    
       //Shift + 'l' to avoid accidental loading
       if (key == 'L') {
         projectedQuads.load(configFile);
       }
    
       //Toggle debug/design/setup mode
       if (key == 'd') {
         projectedQuads.setDebugMode(!projectedQuads.getDebugMode());
       }
     }
    
     public void mousePressed() {
       selectedPoint = -1;
       if (selectedQuad > -1) {
         PVector[] points = ((Quad)quads.get(selectedQuad)).getPoints();
         for(int i=0; i<4; i++) {
           if ((Math.abs(mouseX - points[i].x) < 10) && (Math.abs(mouseY - points[i].y) < 10)) {
             selectedPoint = i;
             break;
           }
         }
       }
     }
    
     public void mouseDragged() {
       if (selectedQuad > -1 && selectedPoint > -1) {
         PVector[] points = ((Quad)quads.get(selectedQuad)).getPoints();
         points[selectedPoint].x = mouseX;
         points[selectedPoint].y = mouseY;  
         //snapping
         for(int i=0; i<quads.size(); i++) {
           if (i == selectedQuad) continue;
           PVector[] otherPoints = ((Quad)quads.get(i)).getPoints();
           for(int j=0; j<4; j++) {
             if ((abs(otherPoints[j].x - points[selectedPoint].x) < 5)
               && (abs(otherPoints[j].y - points[selectedPoint].y) < 5)) {
               points[selectedPoint].x = otherPoints[j].x;
               points[selectedPoint].y = otherPoints[j].y;
               break;
             }
           }
         }
       }
     }
    
    
    
   
   }
   

  So at this point I'm stuck and do not know what my problem is and I would appreciate anyone who can shed some light.

A typical Processing sketch consists in 2 main methods -> setup() & draw().

This is true - so can you provide me a link as to where I can read all of this information? That would be helpful.

Sorry if I seem negligent or like I don't want to take the time to look around. I come from a java background but it was nearly 10 years ago. In the last year I went from openFrameworks to VVVV and now processing. Now that I'm learning yet another new language I'm eager to get started, but because of it's java foundation I feel I understand at the least the basics of Java and OOP and most of the beginner or entry level tutorials are teaching me what I already know so I might not take the time and pay attention to it all. But like I said - I'm willing to learn if you can point me in the direction that would fill most of these knowledge gaps I would definitely appreciate it.

It's just this new format/GUI - it's all new to me so I'm trying to put it all together. - Please bear with me

These are the bare basics:

Looks like you overlooked my "See the Common issues with sketch names article." sentence...
Or the article isn't clear enough. In this case, remarks and suggestions are welcome.

Somewhere along the way I seemed to have missed that one... woops. Good information for someone new to processing.

Thanks. I've managed to make some progress but this stupid script still has syntax issues... Oh well. I'll figure it out.

Just re-publish your current progress and we may be able to help you further!  

Hmmm Okay... So now the problem I run into is here:

//Shift + 's' to avoid accidental saving
    if (key == 'S') {
      projectedQuads.save(configFile);
    }

Error is "cannot find anything named projectedQuads" ... I assume it's because the class is called ProjectedQuads - so when I change the code above to call ProjectedQuads - it leads me to another error.

"cannot find anything named "configFile"... The author of the code had this to say:

"Config file is a global variable to be defined in your sketch. Just like in the example in the .zip you can have 

It's hard to guess what's your current situation is w/ just some code lines.

projectedQuads.save(configFile);

This line is OK, but is supposes you made a variable of the type of your class:
ProjectQuads projectedQuads = new ProjectQuads();
and it supposes indeed you have declared a configFile variable:
String configFile = "some/path";

When you write:
ProjectedQuads.save(configFile);
you make a so called static call, ie. you suppose your save() function isn't using any (non-static) field of the ProjectedQuads, ie. it behaves as a pure function, not as a method (which can use fields / variable of the class).
And the save() function must be declared as static too.
In Processing, (and in Java!) it is generally better to avoid the usage of static methods, anyway.

Very good. With your guys help and some logical troubleshooting I managed to get it running properly! Success :)!

Now I'm on to the next one: SurfaceMapper.

I'm semi following THIS

The problem I get when trying to run the script is "The package 'ixagon' does not exist. You might be missing a library".

So I've downloaded the package twice from https://bitbucket.org/ixagon/surfacemapper , extracted to my documents/processing/libraries/ directory, which is where my sketchbook is pointed. I also, just to double check, drag and dropped the .java files into the 'libraries' directory (as opposed to extracting) just to make sure I was doing it right. Nothing. Of course I restarted processing - I even restarted my computer... Same issue.

"The package 'ixagon' does not exist. You might be missing a library".

As I mentioned in a post way up:

My sketch path is fine.

So... Hmmm. When I download surface mapper, It is a folder 'ixagon' with 5 .java files in it...

Am I missing something? 

If you got it from this link:

Nice. Thank you..

Now I get the error "The type processing.xml.XMLElement cannot be resolved. It is indirectly reference from required .class files"

I downloaded the proxml library and placed it in Documents\Processing\libraries\proxml

And verified that the proxml.jar is in Documents\Processing\libraries\proxml\library

I've imported the library to my sketch...

What else?

And just so you know I really appreciate all the help along the way. Learning how to resolve these errors and what they mean is setting me up for independent troubleshooting in the future :)

Thanks again.

"processing.xml.XMLElement" is not proxml.
It is Processing's built in XML library.
Which has changed a lot between 1.5.1 and 2.0... Would need quite some work to adapt the code, here.