Water comes out of my single lever kitchen faucet, but when I press the sprayer handle only a small, weak spray comes out... from other readings I believe I have a diverter problem... I have a kohler k-10412 faucet...
I need help to clean out the diverter

"i have a kohler k-10412 faucet....i need help to clean out the diverter"

And I wish I could give you specific advice instead of a general description of what to look for. Unfortunately Kohler doesn't furnish exploded views on their spec sheet.
Before you dig into the faucet, check the sprayer head and diverter action.
Unscrew the sprayer head from the hose. Turn on the water, you should be getting a full stream from the open hose. Now place your thumb over the hose, the diverter should divert the flow to the spout. If everything happens like I just said then the diverter's operating OK and the sprayer head's clogged and you won't have to open up the faucet. You can open up the sprayer or simply replace it from your local hardware store. If not you'll have to clean out the diverter.
First remove the handle and pull the spout. You should find the diverter at the base of the spout and just above where the sprayer hose connects on to the valve body. Pull it out and clean out any crud and trash that might be lodged in there. If you pull the diverter all the way out then check to see that the path from the valve body to the sprayer hose connection is clear. Good luck Tom