how exactly would you use the rear end on a lawn mower?
The premise is actually pretty simple. And by using a transaxle, you'll have a direct line of power for that vertical shaft engine you've got sitting in the corner collecting dust.
The act of is kinda complicated, though. Most folks would suggest locking the differential, cleaning out the packed grease, venting and sealing the case, and loading that bad boy up with 90w gear lube. From there it's a simple matter of familiarity with what RPMs your transaxle will handle, setting up your pulleys within a safe, reasonable range, setting up a brake on the axle, and extending it out, usually through some keyway hubs.
So while simple by premise, it ain't exactly simple. There's a lot more than slapping a transaxle on the back and cutting a hole in some grass. And not to sound like the Heymow guys, but they have a real good point when they thump the safety bible and remind folks that the built in disc brake on the transaxle won't get done what you need it to get done. Remember that if you go this route and accept it as gospel.