Adjusting the valves. I thought I'd post a few pics for my fellow noobs on this, since the pictures in the Technical Service Manual you get from Kohler are horrible.
Here's a picture inside the valve cover. I drew a red line across the gaps, where you'll measure your valve clearances.
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Insert the feeler gauge into that gap (look up the specs for your engine in the Kohler service manual.)
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You'll put a 1/2" wrench on the lower unit (it spins freely) and a 7/16" on the nut. Turn the nut to close or open the gap.
For my K341, the intake valve clearance is spec'd at .008" / .010", so I got to the point where the .010 went in just a tad snug, and the .008 passed through easy. I figure I was hitting just about .009 this way.
As a learning curve item, I checked my clearances before I cleaned the underside of the valves and the seats. The intake was easily over .020" (target .009") and the exhaust was over .030" (target .018".)
It's not time to make adjustments until you complete that cleaning. The carbon on the underside of the valve and in the seat is what's giving you this higher clearance. Clean it first, then gauge and adjust.
I think I was getting close to .010" of clearance just from the carbon buildup.