I just dry mine off. If it gets dull it can always be sharpened. Rust is a problem that won't go away quite so easily.

I take the blade when finished shaving, rinse with hot tap water (mine's 140F+). Then I blow through the scales to remove any excess water. I then pinch the blade in the towel, sharp edge up, grasping gently at the spine, and slowly dry the razor. Be careful not to cut yourself!

You can use a can of compressed air available at most any place that sells computer stuff. That can be used to blow out the pivot area.

I typically shave with each razor in my rotation once a week. I've not had any problems with rust. For storing razors long-term, try some Dovo Sterol available from Ray at Classicshaving.com.