I installed that same faucet when I remodeled my kitchen back in 2003. It developed the same type of leak last year. I was highly disappointed that an American Standard product was so shodilly made.
As stated above, turn off the water and pull out the hot/cold cover plug. The set screw is an allen head, and when you losen it, you can remove the handle (provided it is not too corroded inside).
I stripped mine down all the way (there is a collar inside that you need to pop out, and the entire inner workings are held in by a couple of screws). There are no washers, per se, inside. It is a brass assembly with o-rings, springs, seats, and ports. I could not find any worn parts; I replaced the o-rings and it seemed to solve the leak for a few months. But earlier this year, it started leaking again, and I got disgusted and replaced the entire faucet.
One other thought... does that unit have the spray hose attachment? I had an earlier problem with the unit where water would leak past the hose connection at the spray end, and, unseen, drip down the outside of the hose, and end up under the sink in the cabinet. In that case, I picked up a new spray end to stop the leak.
No more AS kitchen faucets for me. --
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