There are 3 known methods to perform guitar vibrato.
1. While fretting a string, twist (or wiggle) your hands(or fingers) left and right quickly, while still fretting the string at the same point.
This is a subtle vibrato. Seen violin players? Its smth like that.
2. Small bend-release motions of the string, using either finger or wrist action. This is a player-defined form of vibrato, can range from narrow and subtle, to wide and aggressive.
3. Although not really considered vibrato, one way to add some wavering or fluctuations in pitch to the note played, is by using the Whammy/Tremolo arm. Again, the range of motion here is entirely player-dependant. Hard or soft? Entirely up to you.
No matter what form of vibrato you use, one thing is always constant. The rhythm and the speed of the vibrato. The speed at which you do the vibrato should be syncronous with the tempo of the song. Also, the vibrato must be even and controlled, very consistant sounding.
Well this is about all I know, my vibrato needs fixing as well... Hope I've helped.