VERY little. Bear in mind that the input shaft (I'm assuming that's what you're talking about) spins around inside the clutch assembly, and any grease/oil on the shaft will find its way onto the friction surface.
A little grease is generally required for the pilot, but again VERY little (you don't want it to squidge out and get all over everything.) The shaft should be dry - or I might use a whiff of dry graphite on the thing - which would be applied to the internal spline on the clutch disc, for more control.
First and foremost - make sure the clutch disc is perfectly concentric - or damn close to it - or you'll be swearing in several languages. The best alignment tool, I've found, is a broken input shaft. Nearly any Jeep manual transmission will work - almost all of them use a 1-/18"-10 input shaft spline. You can cut one off with a grinder (I did.) Those plastic ones have a nasty habit of bending...
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