Normally  a garter snake sheds its skin in one piece. Sometimes this skin ruptures in pieces, but there are no pieces left on the snake. There can be different reason for this. Most heard are the following explanations:

– The terrarium is to dry.
– There is no water bowl present in the terrarium that is big enough for the snake to lie in.
– The snake is ill or underfed.

Personally I think that the first two explanations above are nonsense.  If your snake is healthy and normally fed they will shed their skin perfectly in a dry terrarium without water. That is my experience. I keep all my garter snakes in very dry terrariums and most af them never lie in the water bowl.
When the third explanation is at issue you will have to change the condition of the snake. This is in most cases the reason for troubles in shedding.

So… try to find the reason why the snake does not shed its skin the right way and find a solution for it. Of course you can, a few times per day, spray some water on the snake. Or place a small box with a hole in it through which the snake can crawl in. Fill the box with moist material.
But when you do not find the real reason for the troubles, they will only help just a bit.
Feed the snake with better food or go to the vet if you think the snake is ill.

To remove the skin that is left on the snake you can place it in a box with a bit of lukewarm water in it. Make sure there are some small holes in the box so your snake is able to breathe. Half an hour later the skin can be removes easily. Don’t forget the tip of the tail. If there is skin left the tip can die away.
Also important is the removal of the eye-caps when they are still on the eye after shedding. An easy way is to wrap some Scotch tape, with the sticky site on the outside, around your finger. Carefully push the sticky tape against the eye and normally the eye-cap will come off. Be gentle and do not force it.
Like always… if you are uncertain about it, go to a vet!