First, there’s the axle of the pedal which can be disassembled and lubed with a multi-purpose grease. This shouldn’t be necessary for quite some time, perhaps annually.
Then, there’s the clamping mechanism.
For shimano spd, there are quite a few moving parts that must be kept clean. Clean well and lubricate the springs and moving parts with a good dry lube such as teflon to avoid attracting dirt.
Time atac just has the release bar – one site suggests dribbling heavy oil into the pedal where the bar penetrates.
Crank Bro’s have a very simple mechanism and very little service is required – perhaps a little teflon along the axle where the clamp springs rotate.
Lubing the cleat on the shoe is really only necessary if you’re getting a lot of creaking as you pedal, or are having difficulty clipping in and out. Again, a little dry lube if possible to avoid attracting dirt, and to reduce oily footprints.