Much like you wash your truck to keep it looking spick and span and to prevent potential corrosion and rust from forming, you want to do the same with your cover to extend its service life. But, it all depends on the type of coverage that you install on your truck. No matter, though, it is not going to be a difficult task. The easiest of which would be a hardcover as you would wash it in the same manner as you would your truck. You could even wax and buffer it if you see fit.
As for soft covers with a vinyl tarp, a mild car wash soap and a brush will probably do. Then, top it off with a specific protectant spray for tonneau covers. But, as for waxing this type of material, it may damage the material so you probably want to avoid it.