Jazz can be very daunting to play: all those chords coming thick and fast. But there are sequences that are easy to play over, providing you keep within the same key. For instance, if you are soloing in C major against the chords C, F and G (the 'primary' chords in C) then anything you play will sound OK. Incidentally, this goes for the 'secondary' chords Am, Dm and Em too. Just play the notes of the C major scale and let the chords make you sound good.
Easy? Well you might think so but it can still be hard to play anything. This is like writer's block. Asking a musician to play up and down a scale is a lot like asking an author to type the alphabet on their blank sheet of paper. It's writing but it's not very creative!
But writing gives us a clue. Imagine the instrument you are playing is your voice and use it to say "Humpty Dumpty sat on the wall". Try it again with some different notes. Now you have a musical phrase. Only you know you are really playing Humpty Dumpty.
Now try some other lines you know. Something from Shakespeare perhaps? It doesn't have to rhyme; anything will do. You can tell your own story or describe how you felt on your way to wherever you are playing: "I burnt the toast so I had to make some more and that made me miss my bus and now I'm grumpy." Too long? Probably. So just take one part of it and play that: "I burnt the toast, I burnt the toast." Use another section for an answering phrase: "Now I'm grumpy".
Telling your own story in this way can make it easier to connect emotionally with the music you are playing. As you become practised at this technique you can react spontaneously to events as you play. Whether your audience is the Albert Hall or the rest of your class you can express annoyance with someone who came in late or proclaim your love for the attractive person in the front row. And they'll never know (at least until you tell them).
Having got started with improvising in this way you may find you have an incentive to tackle the esoteric arts of modulation and key change. But that's for a future post.