I did a clinic w/ Steve Vai a few months back and he spent a bit of time talking specifically about how to practice vibrato. Most people don't sit down and practice that - they'll do scales, songs, improvising, jamming, etc. but not vibrato. Your vibrato will eventually develop this way, just through playing, but it may take a longer time; and you may not be expressing what you want because you only ever tried it "one way."
1) Sit down and practice different types of vibrto motions - circular, horizontal, vertical.
2) Sit down and practice different speeds and depths.
For both of these pick a note and get used to working it in different ways. If something feels uncomfortable, that's good - it's what you need to spend time with. Try it with different fingers on different strings all over the neck. Set a timer and sit down for 10-15 mintes JUST working on getting comfortable with a circular motion. Set a timer, pick one note - one spot on the fretboard - and explore as many different ways of doing vibrato as you can. You'd be surprised what you come up with.
While having a "signature," identifiable vibrato is awesome, and it will probably happen naturally over time, it's not always a one-size-fits-all deal. Sometimes you want a slow, smooth warble to the note. Sometimes you want a fast, anguished scream. The goal is twofold. 1) you want to be able to control what you're doing so you can express what you want and 2) you want to explore different things to find what you like in the first place.
