A wobbly tooth can sometimes be fixed through surgery, splinting of the tooth or sometimes a brace.
There's no good way to fix a wobbly tooth at home and it's normal for a tooth to be a little wobbly but you should not have a tooth that is really wobbly.
A wobbly tooth that is really loose could be pulled but eventually the wobbly tooth will fall out on it's own even if you don't pull it.
That is if the wobbly tooth is loose enough.
If the tooth is just slightly wobbly then you should not pull the wobbly tooth as not only will pulling the wobbly tooth cause pain but also bleeding and possible infection.
If you really want the wobbly tooth pulled you should have a dentist do it if it's not loose enough.
However if the tooth is loose enough such as hanging by a thread then you may be able to pull the tooth or at least wiggle it back and forth often enough and they sometimes come loose.
If you have a tooth that is hanging by a thread then you may be able to simply pull the tooth out with your hand.
However I would not recommend doing that as you could cause an infection and get sick.
I would recommend going to a dentist and have the dentist pull the tooth out even if it's just hanging by a thread.
The dentist is skilled at pulling teeth and can easily and more safely pull the tooth out.
But if the tooth is loose enough and you can wiggle it back and forth easily then eventually the loose tooth hanging by a thread should come out.
But if the tooth is causing pain when you try to pull it then don't pull it and just keep wiggling the loose tooth until it does fall out.
I've pulled my own baby teeth when I was 7 years old and was losing my baby teeth.
If you feel pain when trying to pull the loose tooth then stop and wait a while longer.