Specifically for Stone Gardens in Seattle, but will probably work anywhere.
C = climber
B = belayer
When checking to make sure your partner's gear is on correctly, look at the buckles on their harness first, then how the rope/belay device is attached, then at the knot/belay device itself.
The belay device you'll be using is also called an ATC.
When climbing...
Both people get tied in / clipped to the rope.
Then the climber checks the belayer's equipment, then the belayer checks the climber's stuff.
Then, when they are ready to go...
C: on belay
B: belay on!
(the belayer has his hands on the rope and is all ready)
C: climbing
B: climb on!
(now the climber puts his hands on the wall and climbs up)
The climber needs more rope, the rope is pulling too much...
C: slack!
B: ok
The climber is going to fall, or wants to rest...
C: Take!
(the belayer pulls the rope until there is no slack and the rope is tight)
B: Gotcha!
(then the climber sits in the harness)
When the climber wants to climb again...
C: Climbing! (or "im going to climb")
B: ok
The climber reaches the top...
C: Take!
(the belayer pulls hard on the rope until there is no slack)
B: Gotcha!
(the climber sits in the harness and lets go of the wall, now he's ready to come down)
C: Lower!
(the belayer prepares to lower the climber)
B: Lowering
(the belayer lowers the climber to the ground in a controlled manor)
Where I have the belayer saying, "ok", this isn't really verbal. We nod at each other or whatever. If it's not loud in the gym and you're both paying attention, you don't really need to say anything.