If the back fits well, you can glue them up with either PL600 or gypsum plaster. If it's uneven underneath, gypsum plaster is good because you can apply it quite thickly. Otherwise, screws are the way to go, and it's good to find the old studs... At the top and bottom, it usually isn't a problem; just make sure to buy screws for double gypsum. If you tap the wall, you can usually hear where the stud is approximately, and since you don't need to be careful with the old boards, you can make some holes or test drill to find them.