Being that improvisation is largely a spontaneous activity, to think that such an act could be "taught" to someone by another person may initially seem absurd or even self-contradictory. After all, how can you teach someone to be spontaneous?
Classical musicians are used to their teachers giving them etudes to practice, and these exercises are designed to improve or add to the musician's skill-sets. Learning how to improvise, however, cannot be thought of in the same way of learning an instrumental or compositional technique. It's the act of doing something in itself -- more of an attitude or mindset that one gets into while creating music, rather than something that can be explained in terms of its specifics.
If the above sounds complicated and hard, it helps to remember that children improvise all the time with tremendous ease. They will hit things, blow things, pluck and strum on anything they can find, even without anyone telling them to do so -- this is largely because they haven't developed the inhibitions and self-conscious mental blocks that naturally develops as a result of entering adulthood. They have yet to make a distinction between art and life, and aren't afraid to express their creativity in a spontaneous and honest fashion. In many ways, improvisation exists as a way for musicians to revisit the state of mind that they used to have when they were younger -- towards the curiosity, directness, and expressiveness of the child.
So the most important thing to do in any given session is to simply relax and play what comes to mind. Since there are no mistakes in improv, there should be no fear of making them, or playing anything that may sound unusual, inordinary, or even accidental. In a sense, "teachers" of improvisation are only there to bring out what already exists in the student, in an environment free from the threat of retribution. Each session can reflected upon in its own terms rather than pitted against the idealized state of a notated score, which tends to make the activity an uplifting experience, regardless of outcome.