Start with the pulse, which is the underlying rhythm, (which is one of the main things that gives a song its character-if you just pound out the pulse with a stick, it will sound like the song)-- then you can create a variation on the pulse, create a variation on the melody, use a bit of counterpoint theory, and bingo! you've got a great solo!

Then, you can do it again, using different variations, and go on all night--

The trick to this answer, of course, it is only simple if you know your rhythms and melodies well enough to be able to improvise with them. It takes a lot of listening, a lot of practice, and creativity.
Any good teacher can help you to learn the rhythms, scales, rules of harmony, and all, but learning to create is a different situation entirely--