Jazz is the medium through which improvisation is king. The songs that all jazz players should be familiar with are called standards. These standards are know by all and can be called on at any time in a gig . A jazz improvisation is often based on a standard that everyone knows. If you plan to be a instrumentalist, you definitely should attempt to learn the jazz standards. To be a good player, you must know the song and understand the pattern. You will find that if you understand music it can be an invaluable skill when it comes to this task.
The main melody of the song is usually played once through by all members of the band and then the instrumentalist begins. Awaiting your cue to begin your jazz solo, you are well advised to know how long the first section will be. You will receive a nod by the leader of the band to begin your solo when it is your time in any case. Sometimes if there is a vocalist, your solo will begin after they sing.
Great jazz improvisations are based upon time, patience and training. Your solo should follow, sometimes loosely, the chord pattern of the song. This is where all the time you spent practicing scales will bear its fruit. If you learn your scales in all keys and practicing going from one to another, you will be on your way to knowing what a jazz improvisation solo should sound like. Try playing arpeggios if you are having a hard time making up a solo, this may help get you going. A good solo is not simply combining scales one to another. The jazz solo should contain dynamics, structure and have something to say. You cannot plan your solo note by note but you can plan a basic route you will take.
Most jazz improvisations start with at least a general understanding and statement of the melody. If you start too hurried and frantic, it will be hard to build upon that mood. The tempo and tension can then be allowed to increase before eventually resolving to the main melody again. Listen to some favorite jazz solos that you know and see if the pattern is not the same as what we are describing here.
You can learn from other instrumentalists as you build your skills. Listen to recordings and go to concerts. In time you will know what the pattern of a good jazz improvisation is intrinsically without being told.