This question gets asked so much for all cars that I would say it is already answered many times - just go back on previous posts and find one of the answers. Why wait for an answer? This model has a spring loaded idler pully called the tensioner. The pully has a slot in it's metal mount to insert a flat bar or pry bar into (or maybe even a tire tool)and force the pulley away from the belt - push towards the back of the engine. (It may have a 1/2 square hole for a socket wrench.) When you force the pulley away from the belt you can take the belt off any other pully on the engine then release the tensioner and take the belt off all the pullies. Sometimes this is not easy depending on how strong you are and you don't want to let the tensioner slip with your fingers under the belt and pully before you get the belt off. Make sure you have a diagram of the belt's route back on before you remove it or you will be back asking for that and have no wheels for a day or two. Route the new belt correctly around all of the pulleys except the last one which you can get to easily. Again push the tensioner out and slip the belt onto that last pulley. Release the tension on the tensioner The tensioner has a 15mm bolt head, use a 1/2" drive 15mm socket and breaker bar. There is also a long bolt and spacer that needs to be removed from front engine mount in order to get belt completely off engine, you will need to support under front of engine before removing this bolt. A floor jack works great. There should be a belt routing diagram sticker on top radiator support.
THIS APPEARS to be generic answer, not specific to the Delta 88... Please expand on how to remove the three-point motor mount, or which points need to be removed to get the belt to thread through the mount.
Answer... Oldsmobile Delta 88 (Delta eighty-eight). 1995, 1996, 1997, 1998 & 1999. The serpentine belt diagram is in the owners manual, end of chapter 6. You will not have to remove the engine mount, just the one bottom leg of the three legged mount which is really just a spacer, nut, & a threaded post. First support the engine at the oil pan. I used a floor jack and a 18 inch 2x4. The nut is accessed from under the mount and you do not have to remove any plastic or rubber pieces. When I removed the nut, the post came with it (I'm not sure if it was seized, had chemical applied, or was welded). If the post needs to be removed separately, there may be a special tool required as the end is star shaped. I'd try a socket, but gently so you do not strip it. You can get an imprint of the end by placing pressure on the end with your finger.
Remove the post. The spacer then can be removed upward. Put the belt on following the above instructions. Move all tools to the side and test. Once satisfied and the engine is cool, replace the mount leg. The spacer is the hard item to replace,,, Insert it from the top horizontally... the tendency is to align the engine side and diagonally lower the spacer to the mount side. That seems not to work... horizontal twisting the spacer as it is lowered. Insert the post and nut. Tighten the post first if removed separately. Of course, remove the floor jack :)