To make chords sound jazzy, people add the 7th and/or 9th and 13ths to chords. There are many many ways to play 7th, 9th and 13th chords, far to many to go over here. Your best bet to learning how to play these chords is from a chord dictionary or similar.
When soloing over a jazz progression, often the chords will all be in the same key so you can just play one scale over them. Just playing one scale during a solo can sound quite boring after a while so its good to know what other scales you can play over certain chords. Here's a few examples:
Over minor chords:
the Dorian minor scale
the Melodic minor ascending scale (also called the jazz minor)
the Blues scale
Over major chords:
the lydian scale
the lydian augmented scale (the 3rd mode of the melodic minor)
Over dominant 7th chords:
the minor blues scale
the mixolydian scale
the super locrian scale (also called the augmented scale or 7th mode of the melodic minor
Jazz is all about tension and release. for example, in a 2 - 5 -1 progression such as Dminor7-G7-Cmajor7, the G chord is a tense chord that wants to resolve to the Cmajor. Often jazz players will play chromatics/wrong notes over the G7 chord, and resolve it on the Cmajor chord.
right now, I really really suggest checking out Lyle Ronglien's jazz lessons. http://www.harmony-central.com/Guitar/Riff
each free lesson only stays for a few weeks, there are still a few jazz lessons you can check out. number seven has a really good solo and progression that you can learn.
I don't have much time on the internet, I'll try to post some more stuff soon.
Miracle Blade 4: Gibs on touch.