Tips on improvisation:
When you don't have an audience, crank your stereo up to some music that you like--nice and loud so you can really hear the music. Make sure it has some melody and good rhythm happening. Now try to find one note that you can hum along with the song continuously and it sounds like it fits. If you can find the one note that fits, you've found the key that the song is in. You don't have to know the name of the note at first, just be able to hum the tone. Now find that note on your instrument.
Let's say you're playing trumpet or saxophone and you've determined that the note that fits is "D". The D scale contains two sharps--F# and C# so you can play the scale along with the song: D E F# G A B C# D. You can play any of the these notes along with the song. You can even throw in some other notes if you want. You can think of the notes as 1 2 3 4 5 6 7 8, where 1=the first note of the scale (in this case D), 2=the second note of the scale (in this case E) and so on. There are NO WRONG NOTES in improv (some just sound better than others!). The BEST notes to play, most often, are the 1 3 5 and of course 8 which is the octave of 1. It's usually best to AVOID the 4. To play in a dorian minor key, flat the 3rd and the 7th. To play in the blues style, play the 1, flatted 3rd, 4th, flatted 5th, 5th, and flatted 7th.
Most important--just try to jam with the music. You'll play some stuff that sounds really bad. But you'll also play some stuff that sounds OK. Build on THAT!
The example above is for the key of D, but it works the same for all other keys.
Give it a TRY. You have nothing to lose and the ability to jam with anyone to gain. Good Luck and have fun!
Dan