Here are some ideas to help you learn how to improvise. Memorising patterns or licks are also helpful and will be included in these suggestions.
Use scales to start with to give you ideas on improvising.
Use a major scale eg C
1. Play the scale with crotchets
2. Play the scale with quavers
3. Play the scale with a dotted feel
4. Play the scale downwards first
5. Play the scale and go to the note above the top note. (D in the scale of C)
6. Play the scale and emphasise the first, third, fifth and seventh notes.
7. Play the scale and emphasise the second, fourth and sixth note.
8. Play the scale pattern but remove certain notes. Try removing the fourth and seventh (Pentatonic Scale C,D,E,G,A,C)
9. Play the scale and lower the seventh note. C,D,E,F,G,A,Bb,C
10. Play only the first, third and fifth and upper tonic notes. C,E,G,C,
11. Play 1,3,5 and 7b. C,E,G,Bb.
12. Using all the above patterns change the rhythm as in the first suggestions. Also try playing the sequences with your own rhythmical pattern.
13. Make up rhythms to try out these ideas. For example try a quaver followed by a crotchet then a quaver.
14. Try the patterns soft building up to loud.
15. Try the patterns tongued and slurred or legato and staccato.
16. Now try all the above using the C minor scale. Dont forget you have accidentals. Your possible notes are C,D,Eb, F, G, Ab, A, Bb, B.
17. Trying using these ideas and include some chromatic passages. For example try C, C#, D, D# to E to get from C E.
18. Trying leaning on the note just above or below notes 1, 3 or 5. For example D C in the key of C or B to C in the key of C.
19. Use all these ideas but use the chord formations to give you ideas. For example
Major Seventh chords 1 3 5 7
Minor Seventh chords 1 3b 5 7b
Sixth Chords 1 3 5 6
Minor Sixth Chords 1 3b 5 6
Seventh Chords 1 3 5 7b
Ninth Chords 1 3 5 7b 9
20. Try playing only the first five notes of the scale you are using to improvise. Use any of the above suggestions that might be suitable
21. Try using triplets in addition to the rhythms you have been trying.
22. Repeat sequences or ideas you have worked out and move them one two or three steps up or down. See what happens.
23. Syncopate your rhythm. Accent a weak beat instead of a strong beat.
24. Use rests creatively.
25. Try using wide leaps for example sevenths or ninths
26. Trying using ornaments
27. Use arpeggio patterns
28. Use the diminished triad C Eb - F# - A
29. Use the blues scales
30. Use the pentatonic scale
31. Try using the whole tone scale You may not think this sound any good!
32. Try using modes
33. Try modulating to different keys using either the dominant seventh or a diminished chord.
34. Work around chord sequences such as chord one four and five C F G. This would work with either using scale or arpeggio patterns.
35. Try playing slow notes This is harder than expected.
36. Try alternating between very fast and slower passages.
37. Try using notes that wouldnt normally work together. See if you can find a way to make them work.
38. Take a tune you already know and rearrange it. This can be a really good way to start to learn how to improvise. Alter the rhythm and add new notes, change some of the notes. See what happens.
39. Alter the order you play your chosen notes. Instead of C,E and G play E,G C or G,C and E.
40. Listen to jazz recordings or your friends jamming to get ideas. If some one has a great lick ask them to show you.