The following is just how I do it. There will/may be many opinions expressed. Remove magazine. Check for round in the chamber. Remove the slide from frame. Remove recoil spring/guide rod. Remove barrel. Take a dry rag and wipe off the barrel, the inside & outside of the slide and the recoil spring guide rod. Then wipe out the frame and mag well. Then take a cleaning brush(dry/plastic bristle brush)and scrub everything off-internals of frame/mag well, and the interior of the slide(rails, safety lever area, extractor.)
I then take another rag, damp with a clp(FP-10 in this case) along with the same brush but I put a few drops of FP-10 on it and repeat the above process. Except I drop some extra lube on the slide rails and barrel/hood. That's it. My P99 not only looks good but smells good too.
In general, I clean my P99 similar to any other pistol that I have. I use a good bore cleaner in the barrel, and either use CLP or MP7 for the slide and other parts, usoing a tooth brush where needed. For the polymer frame, Periodically (2x yr), I use a good dunk and cleaning of the frame in Simple Green with a thorough drying after. plus lube.
In warm months, I use some Brownells Action Lube (grease) sparingly in key spots on the barrel & rails. When the temps drop to 35F, 25F, and below, I use CLP for lube, keeping all lube away from the feed ramp, chamber, and firing pin area.
I have ~2000 rnds though my P99 9mm.