First the obvious.
Make sure the PTO shaft and the Coupler the shaft fits into are CLEAN!
Lubricate the coupler and work it by hand, pull it back a few times to make sure it's opening and closing fully before you get under the tractor. I don't use grease on the coupler itself since dirt and grass likes to stick to it. WD40 or similar seams to work fine for me. I've had trouble with mine after sitting all winter even though I cleaned and lubed it when I put it away.
Grease the zerk fittings on each end of the shaft.
According to the Users Manual connecting the PTO shaft is the last thing you do, so every thing is hooked up and ready to go except the shaft. You should be able to rotate the shaft a bit to line it up as you pull back the coupler and push it on. The blades may move slightly so make sure belts or blades are not hung up.
Other than that the GR2120 users manual, page 27 simply says...
11. Pull back the coupler of the universal joint.
Push the universal joint into the PTO shaft until the coupler locks.
Tug the universal joint backward and forward to make sure it is locked securely.
I know...sound simple right? Not always in real life, especially as we get older.