The classical vibrato (mentioned above) is sometimes called a linear vibrato. Pitch goes up and down but shallow modulation, easy to do it very fast.
The BB King and 90% rock guitarist's vibrato uses the joint of the first finger as a pivot and the string is rocked side to side. The hand is sometimes said to look butterfly like; the thumb may look like the bodyand the 3 non- fretting fingers look like the wing; hence "Butterfly vibrato". This makes a wide wailing vibrato but it's damn hard to learn. I thought for a long time I was doing it wrong but it's just a case of practice. Now it's easy.
I like the idea of Clapton's method using the elbow to rock the hand up and down simply because it could be combined with a linear vibrato and the combined modulation of vibratos could make quite an interesting sound. I regularly combine tremolo arm and fretting hand vibratos for this reason. If you want to learn about tremolo arm vibrato methods you could do far worse than to watch a live video of Satriani.
If I couldn't laugh at myself how could I laugh at someone less ridiculous?
