Can't put serpentine belt back on after replacing alternator

You didn't list an engine size, and with or without air conditioning. There's six different models of Cutlass. Some are front-wheel-drive and some are rear-wheel-drive. I can tell from the photo, (thank you for including that), this is a front-wheel-drive.

There will be a sticker under the hood with the belt routing diagram specific to your application. Also look at the pulleys. When the belt is routed correctly, the smooth back side of the belt will only run around smooth pulleys, and the grooved pulleys will always have the ribbed side of the belt running around them. If the radiator fan is run by the water pump pulley, that must spin in the direction that blows air toward the engine.

I'll post a diagram for a 2.0L and 2.5L in a Cutlass Ciera when I find it.

This is one of the more popular engines for '88.