You can use an x and an y variable that you set randomly at the beginning and when you press the spacebar.

To store all the typed texts you can use a PGraphics image.

Adapted Code

1. String tekst = "";
2. PGraphics textImage;
3. float x, y;
4.  
5. void setup() {
6.   size(400, 400);
7.   x = random(width);
8.   y = random(height);
9.   PFont font = createFont("Helvetica", 18);
10.   textFont(font);
11.   textImage = createGraphics(width, height, JAVA2D);
12.   textImage.beginDraw();
13.   textImage.textFont(font);
14.   textImage.endDraw();
15. }
16.  
17. void draw() {
18.   background(255);
19.   image(textImage, 0, 0);
20.   fill(255, 0, 0);
21.   text(tekst+("_"), x, y);
22. }
23.  
24. void keyReleased() {
25.   switch(key) {
26.   case BACKSPACE:
27.     tekst = tekst.substring(0, max(0, tekst.length()-1));
28.     break;
29.   case DELETE:
30.     tekst = "";
31.     break;
32.   case TAB:
33.     tekst += "    ";
34.     break;
35.   case ENTER:
36.   case RETURN:
37.     tekst += "\n";
38.     break;
39.   case ' ':
40.     textImage.beginDraw();
41.     textImage.fill(255, 0, 0);
42.     textImage.text(tekst, x, y);
43.     textImage.endDraw();
44.     tekst = "";
45.     x = random(width);
46.     y = random(height);
47.     break;
48.   default:
49.     tekst += key;
50.   }
51. }

Do you want a random position on the screen, or just a random position on that line?
Either way, you'll probably have to take the same approach...

If you want the text to be displayed in different locations, then you'll need different pieces of text.
You can either:

      A: Use an ArrayList to store the strings, and every time that the space bar is pressed, add a new element and take input in the new element; or...

      B: Use one string with the spaces, and split() the string into an array of Strings, then display the strings at random locations.

Either way, you'll also have to create a separate set of data to store the locations of these Strings...

How about you chew on that for a while...

EDIT: Alternatively, you could look at amnon.owed's equally speedy answer...

Thanks! That's really really helpful! It works great! 

Hi all, 

See if smooth() helps...

it doesn't.... :(