How to remove the old grip first
In case you have old grips already on, or want to adjust existing ones, I'll just give a more precise version of the "rubbing alcohol" suggestion from https://bicycles.stackexchange.com/a/8720/34651
What I have been using is the Servisol IPA 170 isopropyl alcohol. It even comes with a little plastic tube that fits perfectly with this application, because you have to insert it in below the existing grip somehow! Here's a sample Amazon link: https://www.amazon.co.uk/dp/B000KHDYB0
I then first start to stick a spoon under the grip to make room for the little tube, then put the tube in, spray some in, then push the spoon further a bit more, spray again and then my grip comes off. Here I used an aluminium spoon, but if it weren't my bicycle I would try and use some hard plastic or wood to avoid scratching the handlebar. Not that it matters much as it will be under the grip afterwards.
The thing dries off quite quickly, and the grip soon becomes firmly placed again.
Placing a new grip would be the same but you wouldn't need the spoon, just spray over the surface directly.
Here's a photo of the product and the start of the procedure mentioned. I wish I could have done a video, but a third hand was missing :-)