Lucky we got a guit-box teacher in the house .
Vibrato is an extremely diverse technique on electric guitar, and can be done many ways. I'll list some different approaches. Watch your favourite players and see if you can spot them doing these things:
-(clapton)lifting the thumb off the neck, and using the forearm in an up-and-down motion
-(bb king)lift the thumb off, and rotate your left hand as if opening a door handle-----that's the way he describes his technique
-go to vai's site if you want to know how he does it (someone else posted the link, it's from his old martian love secrets column. it's a fantastic read, i used to do a lot of those exercises.) circular vibrato is interesting, combining classical and mainstream electric styles.
-yngwie uses a really wild version of bb's technique, where his vibratos are much more wide. I believe he leaves his thumb on the fretboard. (going by memory, haven't watched him in a few years)
There you have it, the best of both worlds. In the blues idiom guitarists often leave their thumbs hanging over the fretboard (watch clapton or BB...hendrix...whoever) for more leverage on bends as well. Generally speaking, when people are having vibrato problems poor form when bending is an issue. I'd recommend surfing over to www.guitarprinciples.com ; signing up for their newletter (i've been on it for years, they don't give it out to spammers), buy their books, go to their forums. If you don't want to purchase their materials, just sign up for the news letter, study the free articles, and use the forums. It's very likely you'll learn tons and be more motivated to play than you ever have been!
Now that I've given you a very general idea on vibrato form (watching guitarists on video and locally will help more), here is a great way to practice vibrato.
-get a metronome (perhaps the most sacred of practice tools!)
-set it to a slow tempo
-choose an 'easy' note to do vibrato with (say 7th fret on the g-string)
-relax your forearm, and execute vibrato. each 'pulse' of the vibrato should occur either twice per beat (8th notes), three times per beat (triplets), or four times per beat (sixteenth notes). The reason for doing this is to garner some control, and reprogram your old vibrato habits.
One more quick note about vibrato: relaxation is the key. If you're tensing up it will never sound good! One common thing between blues greats and shredders alike is relaxation. A smooth, vocal-like vibrato can't be achieved if you're tensing you're arm.
Sorry that was unorganized, but it's almost 2 am, and it's been a year since I've been on these forums. I hope I wasn't a nuissance, and GOOD LUCK!