If it's a modern stainless steel DE blade - just needs soap rinsed off and shake to remove water. Some blades have coatings like Teflon that may be disturbed if fiddled with. There are some people that go so far as to strop their DE blades, and claim added blade life and smoother shaves. I'm not that into extending blade life because they're inexpensive. Carbon steel blades will rust up if left wet.
Some blades, like the Gillette Silver Blue, actually have "Do not wipe blade" printed on the wrapper. I just rinse and keep the blade in the razor. It's gonna get changed in 3-4 shaves anyway. Herm
I wash them off and give a few hard shakes to remove excess water. This should be more than good enough between blade changes.
I'm a strange one here ... after a shave, I remove the blade rinse, pat dry and set aside both razor and blade (separate from each other). The razor gets a swishing bath in a jar of alcohol to keep soap scum off.
I found a small glass jar and added some alcohol to it and after I rinse off my razor in the end I dunk it in the alcohol bath for a few minutes while I finish my post-shave routine and sink cleanup The alcohol displaces water so this way I dont need to take the razor apart at all and it sterilizes also. Then give it a hard shake and I set it on the shelf for tomorrows shave. I have hard water and the alcohol really helps with ward off the mineral deposits but I still have to clean razor thoroughly once per week
I do the same thing. I just give it an alcohol bath and hang it in a stand ready for its next use. I don't touch the blade. I use my blades 2 or 3 shaves then pitch them as they are so cheap. My procedure with blades and razors is virtually identical to PumperNickel-BageL
Since I tried some Carbon Steel blades for my Single Edge razors, I was in the habit of drying them off. I guess I still have the habit, because I take it out, dry it off and store it seperate of the razor. But that just me.