Welcome to Gaia! ::

there are lots of different kind of ways to do a vibrato
but i know two, it is they arm movement and the wrist movement
to improve, wat you mostly have to do is relax your arm, wrist, and hand.

Get a shaker egg and practice making a smooth sound in the same shape that you would make with your hand doing vibrato. Ask your teacher/an older violinist for tips.

xd Im an oboist... I can't help you. xp

Hey. I was trying to improve my vibrato too. I went on youtube and found this great video that helped but now I can't find it anymore.
so I think they said to hold your violin firmly with your chin and shoulder but not too firm. This is to prevent the whole violin from shaking.
Then rest your hand loosely on the neck and hold the violin with your thumb and index and then just vibrato.
I'm not sure how helpful that was. How long have you been playing?

Looser up your WHOLE arm and hand. the only thing holding onto your violin is your chin and the thumb should just be supporting the violin. then just shake the write...its hard to explain...for me...it came naturally...i was never taught it XD i watched someone do it and just learned it...then i took private lessons and made it sound better that was it....make sure you don't work to hard...some violinist have been playing for years and they think their doing vibrato but there hand is to tight. loosen up the hand and just let it flow....i guess thats the word. if you have any more questions, just let me know XD

I hate knocking people, but this is BAD advice. NEVER NEVER be tense, EVERRRRR in violin. I'm learning ricochet right now and never more has this ever been true than perhaps when i taught myself vibrato. All my violin teacher epically failed at teaching me vibrato. So, one summer I went to my local library took out a book on violin technique (really old...and dusty). By summer's end I had a decent enough vibrato, and it's only improved (currently working on speeding it up since I have a slow "baroque" style vibrato..eh).

If I remember what that book suggested (and do this carefully):

I placed the scroll of my violin against the wall with the violin securely under my neck. Then practice sliding your first finger on the A string from B to D and back to B very slowly. Slide 3 or 4 times to the bowstroke. Make sure the violin doesn't break. The point is to relax your arm and wrist. Make sure not to bend your wrist as your sliding (1. it's the fastest way to gaining carpal tunnel over the years and 2. as you increase the speed your vibrato will be uncontrolled and sound "nervous" rather than pretty). Once you gain the ability to slide between those two notes, hand, wrist and arm all moving at the same time with no tension in your hand , do the slides 6 to 8 times to the bow. If you master that, go from B to C sharp, starting at 3 to 4 and increasing to 6 to 8. The point is to decrease the distance and increase speed until you go from a fast slide to, voila!, vibrato. The sliding part is easy. Making sure your hand and arm are perfectly straight and without tension is hard. You can do this exercise without the wall, but I know that when I was learning I needed it because I tensed up so much. But the violin won't (and really shouldn't) go flying while vibrating. To help w/ tension make sure you left thumb is ALWAYS straight but without tension and that there is always a round shape between your thumb and index finger when sliding and vibrating.

Everything about violin is counterintuitive. That's why it's so hard to learn new techniques and hone old ones. We're constantly fighting against the grain. Oh, the things we do for music.