A caricature is a portrait of a person that captures the essence of a person in an identifiable form, and yet exaggerates those features that suggest the essential essence. It has a certain cartoon look to it and the essence that is being exaggerated can be positive or negative. Caricature began in years ago as a form of flattery for the rich. It was done more to show the positive side and to flatter the subject.
In order to draw a caricature, the first step is to study faces. You need to study as many faces as you possibly can. You need to study them in photographs and you need to study them in real life. You should try to visualize those features that make the face unique. In other words, since you are going to capture the essence by exaggerating certain feature, you need to understand just what the essence is. The basic rule of this stage is that you are going to maximize the features of the face that are maximized in the subject, and minimize the features of the face that are minimized in the in subject. If the subject has small eyes, for instance, and you draw the eyes very large, you may make a cartoon looking image, but you will not have captured the essence. It will also be unidentifiable.
Proper equipment is important, and the next step is to make sure you have what you need. A good place to start when learning is with pencil. Avoid #2 pencils and look for 4B or 5B pencils instead. The 5B pencil makes a thick and black line. The caricature is going to have a certain cartoony look to it, and the thick black lines will help accomplish this. Then draw the subject much as you would a regular portrait, but using bold and exaggerated lines and a minimum of shadowing.
You are going to be maximizing the dominant feature that captures the essence of the subject. You should be able to determine what that is from your study of the face. It could be a large nose, large forehead, or a big smile. It could also be a small ears or a weak chin. Your caricature drawing should reflect this dominant feature. If you are seeking more of a cartoon caricature, merely do a bit more exaggerating of that essential feature. Like any art form, caricature takes practice, and when you feel you have practiced as much as you can, the next step is to practice a little bit more.