Relax! Improv is supposed to be fun. If you stress about the idea of making up your own lines, you won't do well at all.
Listen to your colleagues. The responses of others can work as triggers, helping you conjure up lines or reactions.
Release your inhibitions. Do not be afraid to pick your nose or belch, as this may set off a 5 to 10 minute series of conversations with which to improvise.
Be specific in dialogue. Don't say, "I went to the restaurant." Instead, say "I went to Wendy's, had me a spicy chicken, lettuce only of course." The more specific the better, as it instills the setting into the mind of viewers.
Play to your strengths. So many people avoid this for whatever reason, but if you're a baseball fan, massage the conversation to discuss baseball. Then it isn't so much improvising as it is having an unplanned conversation.
Never say "no" to your partner. Saying "no" stunts the growth of the conversation and makes the scene awkward as both parties scramble to come up with a new topic.