Initially soak it good with a medium to high viscosity oil. It's best if you can leave it soak well oiled overnight. Then blot up as much of the excess as you can. By soaking it and allowing it to set, the oil is allowed to seep into the Parkerizing and will better protect the metal underneath. Parkerizing works fairly well when it's well oiled. But left dry it offers little to no rust protection. It's basically designed to trap and hold oil near the surface of the metal.
The biggest problem when trying to remove excess oil from Parkerizing, is it attracts lint. A bit like trying to wipe sandpaper with a piece of flannel. What I found to work really well for blotting up excess oil from Parkerizing, is a well worn piece of leather chamois. The kind they use to dry cars with. You want to be sure to use one that is very stiff and dried out. Don't use them new because the leather contains Tannic Acid. But after they're well worn they make a perfect blotting cloth, and will soak up just enough of the excess oil. And do it without leaving lint all over your nice oiled gun. Depending on how humid it is where you live, will determine how much oil you want to leave, and how often you want to reapply it.