Never worked on a Cavalier but I have done 2 cars with transverse engines (91 Civic and 88 MR2) and Cav is a similar layout. You have to lower the engine/trans but not drop it out completely.
Sometimes you need to unplug wiring connectors depending where they are (trans side at least). Remove the driveshafts, first pop out ball joints and lower strut to LCA bolts.
Remove everything attached to the transmission: clutch and shift linkages, speedo cable, reverse light switch wires, etc. Also you sometimes need to remove suspension parts in the way (Civic needed to do that on trans side).
Remove the exhaust system at the manifold flange and move it out of the way, or take the whole thing off if you can easily (MR2 was easy because it's so short). Drain the trans oil. Double check everything attached to the trans is disconnected, as well as anything on the engine with very little slack (especially wires).
Get a high lift floor jack or trans jack is better, and a cherry picker, or just 2 floor jacks. You *need* 2 separate jacks for this. Loosen the engine mount bolts except the one on the engine side. For example the MR2 has the engine on the right (passenger side) so you would loosen the left mount, as well as front and rear mounts... if the engine is on the left do the opposite. Also loosen the engine to trans bolts but don't remove them yet.
Attach a cherry picker to the engine or put a floor jack under the engine oil pan (with a block of wood between the pan and jack), and lift it just enough to take the weight off the mounts. Remove the 3 engine mount through bolts or whatever is easiest to disconnect them.
Carefully lower the engine/trans as far as it will go without hitting anything. It should pivot on the mount that's still attached, with the trans end pointing to the ground. Support the trans with a 2nd jack or cherry picker and remove the bolts holding it on, then remove it (hit it with a big rubber mallet if it's stuck). Be careful to pull it straight out of the clutch splines without damaging the trans input shaft.
Once you get the trans out the rest is easy. While you're in there replace the pressure plate at the same time, as well as the release bearing (in the transmission bell housing) and the rear main oil seal (take the flywheel off to get to it). If you don't replace everything now you'll regret it later. Remember to use loctite on the flywheel and pressure plate bolts when putting it back together, and use the clutch alignment tool, don't eyeball it. Then put everything back where it came from