The simplest answer is to this is probably "Go spend a few years studying your music and your instrument and in time, you will start to understand how it works"--However, after years of trying to figure things out on my own, I have come to believe that it helps a lot if you know what to look for--

The most important thing, if you are going to improvise, is to learn the melody cold--First, so can play it precisely when ever you need to--but secondly so that you know and can use all of the different melodic and rhythmic ideas in it--

The next thing is to figure out what the "bag of tricks" is for soloing in the sort of music that you do--do they simply ornament the melody with a fixed set of musical figures? Do they substitute scales for parts if the melody? Ascending or descending? Do the scales come out of the chord or do they play against it? Do they substitute arppeggios for melodic phrases?

It helps a lot to isolate the "cadence" of the basic melodic phrase --that is, the rhythmic pattern-- Also to identify the variations of it that occur in the whole melody, and to also find a simple (like a single measure) form of it, and a fuller form(2 and 4 measures)--

A lot of music, particularly jazz, have an antiphonal or "call and response" structure--which means that a short musical phrase is played(often two measures), followed by an answer phrase that has a different cadence--if you don't recognize this when it is happening, your solos will be dead in the water--

A surprising number of solos aren't even variations of the melody--they simply repeat a part of the rhythmic cadence over the chord changes--I once filled in for the bass player in a country bar band that began and ended each set with and instrumental break that was just "Quack-quack here, Quack-quack there, Here-a-quack, there-a-quack, everywhere a Quack-quack"--

The thing to remember is that all improvised music is essentiallly traditional--the elements are passed from player to player within the context of playing the music, each one may add or leave out little bit, and individual practice and work is necessary, but it is a collective thing, and you have to become a part of the community in order to do it--