Here's how it all works at ORD (Chicago O'Hare) as a United Express goon.
Signature runs the ramp tower for the -F and -G gates in Terminal 2 at Chicago-O'Hare, and United has their own ramp tower for the -E gates and the entire Terminal 1 (B&C gates.) Basically they control movement on the ramp because there are so many aircraft pushing back, parking, and taxiing at the same time. Ramp gives you clearance to push back from the gate and lets you know which line you should taxi on when you are on your way in/out of the ramp area. Each ramp control is located in its own little ATC tower on top of their respective terminals.
After ramp, you talk to metering which is like calling ground at a normal airport with your location and that you are ready to taxi. Metering has you monitor the ground frequency and when ground calls you with instructions, you just repeat the runway and your call sign and start rolling. God help you if you call ground and tell them you are ready to taxi, they will make you suffer the wrath!
Sometime while you are taxiing, ground switches you to tower and you either wait your turn in line (not usually more than a couple of minutes since we have the world's best controllers) or, if there is no line, they call you and clear you onto the runway before you get there. Once again, you dont call the tower and tell them you are ready to go, they just call you when you are next up in line.
I know the question was just about ramp towers, but I figured I would throw in the big picture of how the ramp fits in with the rest of the operation at the world's busiest airport. (Eat my shorts, ATL, haha) It is a bit overwhelming the first couple of times, but when you get used to it, our system is a very efficient pilot-controller machine that gets a lot of airplanes off the ground in as little time as possible.
As far as staffing goes, I don't know.....I heard once that some of the ramp controllers are retired FAA controllers from Chicago.