Every finger, every string
A vibrato learned on one finger doesn't come free on the others. Each finger has a different length and strength; each string sits at a different angle to your hand. So the ladder gets run on all of them — and two combinations are noticeably harder and get extra time.
Start where it's easiest
1st and 2nd fingers, on the A string. They're the strongest, the A string is comfortable to reach, and results come quickest there. Get a loose, even vibrato on 1 and 2 first, on A, before you spread out.
How to play it
Slow bow, one per note, or no bow. Keep the fingers you're not using resting lightly on the string — especially behind the 4th finger, they give it support.
The two hard ones
The 4th finger. Shortest, weakest, and it has the least natural give. Use arm vibrato for it rather than wrist, and let the 1st, 2nd and 3rd fingers rest lightly on the string behind it — they brace the hand so the little finger doesn't have to stiffen to stay put. The 4th-finger vibrato is the one that, left unpractised, quietly ruins slow movements later. On the G, D and A strings the 4th finger lands on the pitch of the next open string (Stage 1's same-pitch check), so that string rings sympathetically while you wobble — practise on the E string too, where the 4th finger has no open string above it to ring.
The G string, and the E string. On the G string your hand and arm are rotated further under the violin, which changes the direction of the motion; on the E string there's less room and the hand tends to creep over the fingerboard. Both need their own reps — don't assume the A-string vibrato transfers.
Try
The four-finger climb above, on the A string. Then the same four fingers on the D string. Then — a bit later in your practice week — on the G string and the E string. Two or three minutes, rotating which string you start on so the G and E strings aren't always last and rushed.
Hear it
The engine can't play any of this. But listen to a slow movement — the Adagio of Mozart's Violin Concerto No. 3, K.216 — and notice that every sustained note has vibrato, on whatever finger and string it falls, evenly. That evenness across the whole hand is what these reps are for.
The usual mistake
Only ever practising vibrato on the 1st and 2nd fingers, because they work — so the 3rd and especially the 4th finger never catch up, and the first time a slow piece asks for a vibrated high note on the 4th finger it comes out stiff and flat. Give the weak fingers more time, not less.