How do I do vibrato on a violin?

First make sure you have good posture. Stand/sit up straight. keep your left elbow from resting on your side. Keep your left elbow nice and far counterclockwise under your violin, and keep your fingers on their tips.
It is easier to learn vibrato in 3rd position and on your second finger.
Start slowly slowly slowly moving one of your fingers back and forth on a long note. Do this with each of your fingers, and slowly slowly slowly increase the speed of your finger motion.

You twitch your finger on the string in a certain way. Just keep trying, it will soon become second nature.

Put your finger on the string and then without losing contact or changing the tone. Make your finger vibrate, and then move it back and forth. The tip must remain firmly placed and not move, but the movement of the rest of the finger will change the flat sound to a more pleasing vibrato.

You might like to have a look at violinmasterclass.com
This site helped me get started with my vibrato. Remember that your vibrato is flat. natural,flat, natural....NEVER sharp ; do NOT go above the note.
Start practising your wrist vibrato in the third position before trying it in the first position. Let your hand fall back then return...back then return. Start off slowly and gradually work up to speed.It may take a few weeks ; just do five or ten minutes per day.
Get your wrist vibrato sorted out before you start with arm vibrato.

PS the problem I was having was that I was never holding the violin correctly with my left hand. As soon as I corrected that problem then the vibrato became much easier.Make sure you have got your left elbow well under the instrument and not close to your body.

Make sure you have a good shoulder rest and are holding the violin firmly w/your jaw. Then go into fifth position so that the palm of your hand is on the upper bout of the instrument. Place your 2nd finger on the wood of the instrument and then start the motion at the elbow "hi-fiving" your instrument. When that feels natrual, stay in the same position, and just move the finger over onto the fingerboard (still use 2nd to start). Then come back into 1st position keepig the same motion. When in doubt, go back up into 5th and repeat the process. This gets the arm vibrato going first and then the hand vibrato will come later. I find several students get messed up vibrato by focusing entirely on hand/wrist first! Work 2nd finger, then 3rd, then 1st, then 4th. Make sure nails are cut, you are on your fingertips, and placing one finger at a time.

ok this works ... put your left hand up as you were holding your violin ... grab your left wrist with your right hand now extend your index finger of the right hand up the tip of your finger up and by between the index and second finger of your left hand knuckles .... now make sure your left hand is relaxed and let your right hand index finger push your hand .. this is the wrist vibrato movement ... let your finger do the work then try getting your left hand to move like that .. it will take many tries to completely transfer that to the violin but this works

Grasshoppercookie's answer is the first time I've seen real instruction on violin arm vibrato that I'm going to actually try

See:

Can you give me some advice about how to play the "wiggly thing," i.e., vibrato?
http://beststudentviolins.com/PedagogyTe...