I find arm vibrato most reliable, even though I use mainly wrist vibrato. Arm vibrato gives you a nice even vibrato on both single notes and chords, while wrist vibrato can't do chords very well. I don't know how the finger vibrato works (can someone explain to me?) It's used for high positions where you can't move your whole hand.
For all types of vibrato, the most important thing is that you must be relaxed. A common misconception is that vibrato is something tense. You must be relaxed for you hand and fingers to be flexible, then you can move, then you can vibrate.
for arm and wrist vibrato, the goal is to roll your finger back and forth on the string in an oscillating motion. In arm vibrato this is achieved by using the elbow to move your whole forearm back and forth. Wrist is moving the wrist while your elbow doesn't move.