On my wife's 3913 and my 6906 we clean all parts with a good scrubbing of Hoppe's. Next, we blow off the parts with Brake Clean and let them dry.
Re-assemble the frame with a light wipe of oil on all pivots/shafts. A drop on each of the 3 lever plates and one in the spring holes. Don't forget the reset plunger hole. Drop of oil on the hammer pivot and trigger pivot from underneath. Wipe all springs and steel internal parts (trigger bow, etc) with oil.
Assemble with slide the same way with a light wipe of oil on the firing pin and spring. Oil the plungers and the safety/decocker pivots. Put a drop on the extractor too.
I use grease on the rails instead of oil because I prefer it. It has a better ability to prevent galling than oil does. So, a light wipe of grease on the frame rails AND the rails on the underside of the slide. I also put grease on the slide along the bottom of the FP housing. After assembly, I also wipe a light film of grease around the barrel where it meets the barrel bushing. Note here: the amt of grease I use doesn't mean slopping it on. I use just enough to lubricate and nothing more. In most areas, you can't even see it other than as just a film.
Wipe down after function check with paper towel followed by a silicone impregnated rag. (I know it's SS but I do this for ALL my guns, even the blue ones, and I have no rust problems - EVER.)
My semi-auto guns have run this way with no abnormal wear through several thousand rounds so far.
