Somewhat of a tough question. I use them all the time, but explaining it is something else. This isn't going to be terribly steeped in theory, but my perceptions having used them for a long time. Frankly, all the notes work. If you just play them going almost anywhere to anywhere without hanging on a note too long, they are just "passing" tones and the feel of movement is all you are dealing with as long as you resolve in some convincing way. If you start hanging on a note, it will start to have more harmonic significance and, in the type of theory we are discussing, probably offer fewer options.
Some examples to try; Play a Dorian mode starting on A.
A Dorian mode in a is: A B C D E F# G
Some ways I would possibly divide up the notes to consider as pathways are;
A B C C# D E F# G resolve on the octave A.
A B C D E F F# G resolve to octave A.
A B C D E F# G G# resolve to octave A.
That's very basic. You don't need to play all the notes in order or in the specific clusters I noted. Pick out little phrases and try to fill in with some chromatic runs. The fact is, you can start almost anywhere, it can be on one of the tones outside the mode I cited and the notes do not have to be in chromatic order. The key for me is just to create motion, make sure it has some sort of interesting phrasing and then resolve in some way you can "sell it".
Try this riff. It will be in A minor, start in the fourth position with your pinky on A on the D string. You are going to start on the note F# on the D string. Might help to have someone strum some A minor chords or record something to hear it against.
String: D D D D G G D D G G G B B B E
Finger: 1 2 3 4 1 2 3 4 1 +1 3 1 3 4 1
Hope that helps a little.