Learn what improvisation implies. Many think it simply means the ability to think of jokes on the spot, but it is a bit deeper than that. Improvisation, to many actors, is the unscripted response of the character in a new setting. Now, this doesn't mean you need to become a method actor to perfect everything, but not every improvisation needs to consist of hilarious jokes, one after the other.
The first real tip after grasping the idea of improvisation is to start small. Watch your brother play a sports video game or turn down the volume on a real sports telecast and try to be the announcer, discussing whatever comes to your mind. Announcers improvise all the time, discussing whatever they see on the field.
Play the questions game, wherein yourself and a partner have to act out a scene while only asking questions. The fact that you have to concentrate on asking a question should quell the nervousness that comes from having to think on your feet.
If the improvisation is for a TV show or movie, learn the character inside and out. If you truly understand the character, then whatever comes out of your mouth in a given setting should make sense.
Never give one-word answers. Improvisation isn't necessarily akin to stream of consciousness dialogue, but you want to have some form of dialogue.
Have fun. Don't put it on a pedestal or think of it too seriously. Then you get the "ips" and become more worried with how you sound than whether or not you're succeeding.