I am a beginner violinist, and I want to learn to do a vibrato. I know up to 5th position, my intonation is pretty good and I have no problem shifting back and forth, in that contrary, I enjoy shifting. I know this question has been asked before, but none of them satisfies me. I struggle to do a vibrato, and I don't know what procedures I have to follow to do a proper wrist vibrato. I also want to know if there are exercises to do before doing a vibrato.
Vibrato is exceptionally difficult to learn correctly just from reading about it and watching videos. You can get started that way, but ultimately having a teacher or coach help with the physical aspect is usually necessary.
One of the challenges with learning vibrato is developing the use of muscles and motions that aren't ordinarily used in the hand, and probably most difficult, getting muscles that you don't use to fully relax, especially in the wrist. This is where a coach or teacher is important.
Having someone watch and evaluate your current technique lets them instruct you on where you are correct, and help determine what exercises you need to make improvements.
"How to learn and develop vibrato" is probably too general a question for the limitations of this site, as many books and materials have been written on the subject. You can find a multitude of techniques and training practices to experiment with to help you down the path before consulting an expert.
I personally don't call it "wrist" vibrato. With the technique I was taught, most of the motion comes from the upper palm of the hand, a little from the fingers, and the idea that the wrist is fully relaxed and loose (no muscle tension) and reactive to the motion of the upper hand.
The problem with starting to do wrist vibrato is that of co-ordinating right and left hand. To succeed they have to move independently in different directions. It is a bit like the problem of rubbing your stomach while patting your head (which I now see is much easier than it was before I learned to do vibrato!).
The problem when you start is the usual one for new physical skills that it takes up a lot of mental bandwidth and that interferes with the other stuff like bowing. The solution is the same as it is for other physical stuff - practice until the left-hand movement is sufficiently grooved-in that it takes up only a little mental bandwidth and you can do the other stuff, bowing, at the same time.
All the exercises you will see are aimed at helping you do this by building up the left hand movements and then repeating them over and over again until it becomes second nature.