What is the best way to intall a tub surround? The green board is already up and primer. There are no instruction to be found. What preparations do I have to do first? Do I have to use mineral sprits on the backing before I apply the adhesive?

If it's the 5 piece where you have 2 corners, a side wall piece and a front and back wall piece you want to plumb and install the corners first. Then the side wall piece, the back piece, then the front piece where you have to cut around the faucet handles.
Dry fit the wall pieces first before you glue and stick.
You didn't have to use mineral spirts to clean anything as far as I know. Just use the construction adhesive made for suroounds.