hi im a music student of the tender age of 16 however i consider myself to a fairly good musician (emphasis on the fairly haha) and i just thought id write i little guide to improvisation, if not to help anyone else at little it drills mymethods in too my head!

i apologise if any of the following is deemed wrong and any feedback or tips would be of great use cheers!!

improvisation? so how do i do it!
well first lets take a look at the chords you've been given (presuming this isnt free jazz of course)usually they'll be insome progression of somesort, take a look at it try and remmeber it becuase these are you buildig blocks for you "blowing"
first take a look at the root of each chord,so for example Adim7, for now just look at the A, if it helps just play through the improv section playing only the route untill you get used to it,

now take a look at the rest of the chord, in the example above (Adim7) this will be the demished7 bit, thik of this combied withtthe route as you skeleton to your solo, this chord is madeup of the "main" bricks you need to build your solo,
try playing through the arpegio of that chord a couple of times and start to add various rythms, techniques and mix the whole arpegio up a bit

now youve got the basis or skeleton of your solo, you can now add any note that corresponds to that chord in too your solo
for example if the chord is C7 then you can play any note (apart from b natural becuase its a major 7th) from the c major scale and you can also play a minor 7th which is B flat

you can also use modes in your improv. for example C half dimished7 consists of C Eb f* Bb all these notes are contained in the locrian mode played on C (i think, dont quote me on that one!)

so basically to sum up, to improvise play any note that corresponds to the chord weather it be in its scale, arpegio or a corresponding mode but that doesnt mean you cant play any other notes that dont correspond to the chord, its all about tatse,some people like dissonance some dont

eventually oyu wont have to go through this thougght path you'll see a chord and automatically relise what notes "go where" ect and you'll be able to blow to your hearts content

i hopoe this has helped if not im sorry

cheers
jak

ps this is no definative guid on improv im just sharing my methods please do not deem this as the perfect method ect
just trying to help

feedback would be usuful
cheers
jak

Hay there i just thought id give my bit on the matter

Im a jazz musician aswell...i play sax and piano and i agree with you jake but i also think another key point you should look at to further your improvisation is different blues scales eg: G,Bb,C,C#,D,F,F#,G

just transpose it for each key.

and another good mode to impro in is dorian and also try some penatonic stuff that can be fun...it really helps later on and lotsa mucking around helps
Ps: listen to keith jarret or watch keith jarret(art of improvisation) its taught me alot

hey cheers, i use blues scales alot there rather fun
and a good old pentatonic when it comes to rock and the like is definatly a wise choice

cheers for the feedback
jak