You didn't say if it had a V8 or a 235 Stove Bolt 6 cyl. in it. If a V8 or a 1963 and later 250 or 292 6 cyl. it is simple and straight forward, if a 1962 and earlier 235-6 cyl. it is more involved.
V8: a short shaft (tail shaft is about 6 inches long) should should fit right in and be the correct length. If not maybe one out of a chevy truck would be better (medium shaft is about 10" long). measure from the top of the top mounting surface of the bellhousing (mounted on the transmission) to the end of the tail shaft, if it is close the driveshaft may not going to need be lengthened or shortend.
Remove the bellhousing from the engine (6 bolts) then remove the clutch assembly (pressure plate, clutch disk, and flywheel).
Next when you get your TH-350 get a flexplate, shift linkage, brackets and ALL bolts as some bolts are different lengths between auto and stick.
Bolt the flexplate onto the crankshaft and the transmission onto the engine and the crossmember. use a new transmission mount.
The stick transmission and Powerglide automatic transmission used a course splined output shaft and the TH-350 used a fine splined one. You will need to change the driveshaft yoke. This is a good time to check the U-Joints as well.
If you have a Stovebolt 6 you will need an expensive adapter to Mount the TH-350 and you may find it cheaper to swap over to a later model engine.
If this is the case you may find an old caprice or impala or truck that is running to pull all the parts you need with all brackets and everything.