Use a waterproof adhesive for the job!
Some are glued and some are just locked into the corners by way of the design. You need to make sure the wall is even so there are no bumps if you have to glue or they will show through. There should be instructions with anything you purchase.
It will depend on what you have behind the old insert. Most panels are rather flimsy so you will need waterproof drywall behind them. We installed some in a mobile home a couple of years ago over the existing thin sheetrock using PowerGrab. Use some type of tape that isn't very sticky to hold it in place. My husband had some from an automotive store that left no residue when removed. I wish I knew what it is called because I'd like to get more but we haven't had any luck.