Cutting surfaces?

I'm trying to make a cut through some surfaces. There are two kinds:

1. A planar cut (like taking a section view, except I want to actually delete the entities)
2. A hole or slot into a surface.

I'm sure it can be done, but I just don't know the tool I should be using. I hoped it would be the same as making a cut through a solid part, but the insert > cut menu is not available... Anyone know what I should be doing?

Thanks, Sven.