Putting the serpentine belt back on a chevrolet 1987 cavalier 4 door sedan

looking at diagram 2.2l engine to remove belt tensioner held in place by two bolts dont remove center bolt to tensioner just the two side mounting bolts one on each side.

timing belt replacement is a little tedious.
first remove negative battery cable and move away from battery.
remove serpentine belt and set aside.
on models with A/c remove compressor and set aside, then take mounting bracket off.
going through the fender well behind the tire remove the lower pully
with a torx wrench.
remove the cover for timing belt. it goes all the from top to bottom.
this is when you line up the timing marks to make it easier to reassemble.
There is a belt tensioner on the timing belt toward the rear of car.
loosen and the belt will come off.
When you put the belt in and set the tensioner make sure the timing marks are aligned.
clean the old gasket off the cover and put in a new one to avoid leakage.

It's alternator. Do you have a serpentine belt or seperate belt. If seperate, there are two bults on the alternator. Loosten both but do not remove. Take a prybar and pry back on alternator. Have someone hold the prybar while you tighten or hold yourself and tighten. If you have a serpentine belt, you need to replace the belt tensioner. The spring is weak inside the tensioner. It's 30 years old. remember that.

I think you are on the right track, suspecting the tensioner. It should spring back after you release it. There is a pretty heavy spring inside, it may have broken.

You should have a diagram of the belt installation on the radiator support, usually a sticker.
I found your owners manual online but there is no reference to the belt. You may have to buy a Chiilton's or like manual from Orielly's or Autozone to get the pattern. Most serpentine belts use a tensioner and it
has a big bolt in the middle of it that you can put a wrench on and pry it to the side that makes the tensioner loosen off the belt and then slide the belt off the tensioner or other easy to reach pulley. You should nbot have to remove any bolts. That was the whole idea of the sepentine. A tensioner to keep it tight and easy removal and replacement.
Here is the site for the manual.
http://www.extendedgmwarranty.com/owners-manual/chevrolet/1998-Chevrolet-Cavalier.pdf

Don't know what size of motor you have but this should help you:

Removal & Installation

1. Loosen the accessory-to-mounting bracket bolt(s) and adjusting bolt.
   
2. Rotate the accessory to relieve belt tension.
   
3. Slip the drive belt from the accessory pulley and remove it from the engine.
   

If the engine uses more than one belt, it may be necessary to remove belts that are in front of the belt being removed

To install:

If the engine uses more than one belt, it may be necessary to remove belts that are in front of the belt being removed

1. Place the new belt over the crankshaft or drive pulley and stretch over the driven (accessory) pulley.
   
2. If removed, install the other belts in the same way.
   
3. Adjust the belts to the proper tension.
   
4. Tighten the adjusting and mounting bolts.
   

Models equipped with the V6 engine and most 1987-94 engines use a single (serpentine belt) to drive all engine accessories. The serpentine belt driven accessories are rigidly mounted with belt tension maintained by a spring loaded tensioner assembly. The belt tensioner has the ability to control belt tension over a fairly broad range of belt lengths. However, there are limits to the tensioner's ability to compensate for varying lengths of belts. Poor tension control and/or damage to the tensioner could result with the tensioner operating outside of its range.

To replace the belt push (rotate) the the belt tensioner and remove the belt. Use a 15mm socket on the 4-cyl. engines and a 3/4 in. open end wrench on the V6 engines.
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Usually under the hood or somewhere in the engine compartment there is a belt route diagram. Hope that helps.

put belt on all pullys excpt water pump do it last

You can run down to your local auto parts store and buy a serp belt tool. Or you can take a 3/8 drive ratchet, locate the 3/8 square hole in your tensioner and put the ratchet in the hole. For more leverage I put a deep socket over the ratchet handle and put a long 3/8 extention in the deep socket. This will provide ample leverage and will save buying more tools you do not need. Simply move the tensioner to the direction that takes pressure off of the belt.

there will be a diagram of the routing of the belt on the bottom side of the hood. You need to specify what engine you have also. One common thing is the tension pulley, you will need to pry on it to relieve tension in order to put the belt on. Make sure you save the alternator for last as you can get to it a lot easier that the rest.