When climbing multipitch, what is the cycle of things you do when climbing each pitch, and what are the associated voice signals?
Alice and Betty are climbing in a team of two. Let's start the cycle with both climbers together at a belay, both tied in to the anchor with clove hitches. Betty is going to lead the next pitch. The standard set of voice signals in America, which I'll use below, are the ones introduced by Paul Petzoldt. When the climbers address each other by name, it's so that there won't be confusion between different teams that are near each other.
Betty gets together all the gear for her lead. If Alice and Betty are alternating leads, then Betty's end of the rope is already on top, and if they're using two cordelettes to construct their anchors, then Betty already has the cordelette that she cleaned from the previous anchor. If they're not swapping leads, and this will be the second pitch in a row that Betty is leading, then the rope needs to be flipped over, and Betty needs to get the other cordelette from Alice.
Betty: "On belay?"
Alice puts Betty on belay. "Belay on."
Betty unties her clove. As a courtesy or in case it isn't clear, she can say "Climbing," to which Alice would answer "Climb."
Betty does her lead, gets to the next belay station, builds an anchor, and ties in.
Betty: "Alice, off belay!"
Alice takes the rope out of her belay device. "Betty, belay off!"
Betty pulls up the rest of the rope. When it's taut and pulling up on Alice's harness, Alice yells, "Betty, that's me!"
Betty puts Alice on belay. "Alice, belay on!"
Alice takes the anchor apart. When she's ready to climb, she yells "Betty, climbing!" so that Betty has a heads-up to expect that she needs to start pulling up rope. Betty responds, "Alice, climb!"
Alice climbs the pitch, cleaning the gear. When she gets to the new anchor, she ties in. "Off belay."
Betty takes her off belay. "Belay off."
For situations where voice communication may be impossible, and the climbers may not even be able to see each other, they should discuss in advance how to handle that. Some people use systems of rope tugs, but in my experience those don't work very well. If the leader yells down "off belay" but there is no communication, then they can just pull up the rope slowly while the follower continues to feed it out through the belay device. If this type of situation is anticipated, then sometimes they will discuss this in advance, and the leader will just promise to put the follower on belay within a few minutes once the rope feels taut. If the rope may not be long enough to finish the pitch, sometimes people will agree in advance to simulclimb a short portion at the end so that the leader can reach the belay.
The German mountaineer and safety expert Pit Schubert advocates to reduce the signals down to two:
(I'm reusing @Ben Crowell's terms since I know only the German words)
- Leader to belay: "Alice, off belay" (German: "Stand!") when the leader has built their own anchor point. If there is a line of sight to the belayer, the leader may also show both hands as a clear signal that they don't need them to climb anymore.
- Leader to belay: "Alice, belay on" (German: "Nachkommen!") when the leader is ready to belay the second climber.
All other commands are redundant.
For Great Britain, with both climbers beginning at the foot of the next pitch, with leader
L and second
LOn belay: I'm tied to the rope and prepared to climb
SClimb when ready: I am now belaying you
LClimbing: I know you're belaying me; expect to pay out now
LSlack (or rope colour), Take in, or Tight as needed during the climb; also Below! when required
LSafe: I'm attached to something solid, you can stop belaying
SOff belay: Rope is now out of the belay system
LTaking in: I'm pulling up the slack
SThat's me: You've finished taking in
LClimb when ready: I am now belaying you
SClimbing: I've cleaned the stance, and am starting to climb
That's the full set, but there's no need to be so chatty all the time, especially when we can see each other; conversely, when the conditions are difficult, the situation often has to be inferred (see imsodin's answer).
There's a couple of extras I use as a second, especially on winter routes: ten metres! and five metres!! when I'm concerned the leader hasn't yet found a belay stance.
@BenCrowell describes the sequence nicely and @Jasper brings up reducing commands. Due to circumstances (no visual contact and out of earshot) and simply to reduce the yelling on the mountain (both for the pleasure of silence and security, as there is less that could be misunderstood, especially on crowded sections) it is beneficial to do so. I'll give an explanation why you need no signals in the cycle to stay safe (and also which signals I consider still beneficial and why).
There's two safety-critical moments:
Leader reaches next belay, sets it up and secures themselves ⟶ can be taken off belay.
Leader takes second on belay after pulling up rope, such that they can clean the previous belay.
Now lets assume you can't give a signal as you can't see or hear each other. Rope tugging signals aren't reliable either due to rope drag. How can you ensure swift continuation of the climb while staying safe?
Second just keeps belaying until the rope is up. Tedious, but safe. This reduces calling "off belay" to an efficiency measure.
The leader sets up everything for the belay before pulling the rope up. Then once they feel the end of the rope, they purposely leave some slack. Then finish setting up the belay with the rope and pull in the remaining slack, tightening the rope strongly. Thus the second knows they are on belay once the rope is constantly taught. This is good practice even if you use a command, as it reduces the time the second could make a mistake without being on belay.
Essentially if I can give a signal, I always give the "off-belay" command, as it speeds up pulling up the rope. I don't give "on-belay" commands (except of course my rope partner explicitly requests it, in which they'll have to listen to a sermon about the virtues of not doing so after the climb :) ).