Watch comedy talk shows on television, especially the Comedy Channel and programs where stand-up routines are a regular part of the fare. Write down lines that you think are especially funny, or ones that get a big laugh, even if you don't understand them completely, when you hear David Letterman or Wanda Sykes say them.
Take the joke apart, to understand its components. For example, listen for words and phrases, such as "What about" or "Did you hear" and learn to recognize the set-up. Then see what comes next as the body of the joke, usually a story. Finally, listen for the punch line. This is what gets the laugh.
Try a simple knock-knock joke on your friends. Most will know to answer "Who's there?" Then you must respond with a one-word or two-word answer -- to which they will say that word, or words, followed by "Who?" -- and then you will say the punch line. See the list of clean Knock-Knock jokes in Resources, for practice.