The action at fingertip level on the fingerboard is almost a rolling motion. The fleshy tip of the finger - not the flat part - is the bit to use and this is why fingernails MUST be kept short, and I really do mean SHORT. No overhang of the fingernails, otherwise you'll play with flat fingers which makes vibrato impossible.
Whether the main part of the vibrato is arm or wrist, the only way to achieve it is through being relaxed. Any tension whatsoever in the shoulder, arm, wrist or hand, will have a negative effect. The fingers must also remain supple and yield to the movement in the arm and hand.
Main cause of a lack of vibrato development: TENSION!!! Don't grip the violin neck with the thumb and first finger; if you feel you have to do this in order to keep the violin in position, then the shoulder and/or chinrest needs adjusting so that the instrument will remain comfortably in position even when you let your left arm drop down by your side. It should be adjusted so that the weight of your head alone on the chinrest holds the violin steady - no squeezing or having to clamp it in place using pressure from your jaw.
Vibrato should begin to develop naturally once you feel relaxed and at home with the instrument, and your playing. Vibrato adds expression to music, so use it that way. Not every note needs it and vary the speed and width of the vibrato used according to the piece and the emotional effect you want to create.
QUOTE
Try supporting the scroll against the wall (or get someone to hold it) to give the fiddle some supprot while you wobble
Sorry to be picky here

, but describing vibrato as a "wobble", is what often makes students produce just that, a forced "wobbling of the note". The intonation should remain fairly central and the vibrato either added to the note and above (predominantly in sharp keys), or to the note and slightly below (predominantly for flat keys). Wobbling tends to be born out of tension, a vice like grip, as I've already mentioned. Free the thumb and the knuckle joint of the first finger from the neck and it will develop into vibrato. A forced wobble under tension will always sound like a wobble, especially to a listener.