Sure.

The unsophisticated way allocates a distinct object name for each bird:

Code:

Bird myBird1 = new Bird();
Bird myBird2 = new Bird();
Bird myBird3 = new Bird();
 

The slightly-more-sophisticated way, which lets you adjust the number of birds in your sketch fairly easily with small code edits:

Code:

Bird[] myBirds;

myBirds = new Bird[100];

for (int i = 0; i < 100; ++i) {
    myBirds[i] = new Bird();
}
 

The slightly-more-sophisticated-than-that way, which lets your sketch handle a number of birds that you don't know as you're writing:

Code:

List<Bird> myBirdList;

myBirdList = new ArrayList<Bird>();

for (int i = 0; i < 100; ++i) {
    Bird freshBird = new Bird();
    myBirdList.add(freshBird);
}
 

What you're wanting to do is exactly the reason that "classes" exist at all. I'm not sure how you could know what a class is, and not know how to instantiate instances of said class.

To understand the basics of object-oriented programming, I recommend taking a look here:

http://processing.org/learning/objects/