The most useful signals when everyone is moving are those indicating direction to those behind (if a lead paddler decides he hasn't picked the best line he will often signal to those behind to go left or right), or a need to eddy out and wait. Usually pointing with the hand (maybe jabbing it frantically to make it more visible or if the paddler hasn't much time before needing to use his paddle). If preceded by the "eddy out" signal (hand held up and circled around, often with index finger raised) the directional signal suggests which side has the better eddy. In an ideal world, the lead paddler would have eddied out either to one side or mid-channel to give himself time to give the signal and be sure that it had been seen. That isn't always possible and if a signal is given quickly or the group is well spread out, not all following may see it. It's important therefore that if you see such a signal, you should repeat it to relay back to those behind and if possible check that it has indeed been communicated.
Once static, the person ahead may want to indicate that a single person should move down the river. A hand/arm held vertically upwards indicates "one person to move". It may be preceded by pointing to a specific person (in which case the signal won't be given until sure that the intended receiver has realised that the signal is for him). Watch out for following signals if the leader wants to indicate a specific line to take or to grab a particular eddy. If visibility is restricted, a paddle held vertically may indicate the same thing - be sure to hold it up steadily for a while so those behind can be sure it is a signal and not just someone out of sight using the paddle vertically. This is particularly useful when the leader can see the bottom of the rapid and wants to bring others down one at a time from an eddy where they can't see what has happened to those in front.
Often the first person at a rapid grabs an eddy with a view and then wants to move another experienced paddler down to an eddy further on or to the bottom of the rapid to provide safety cover. That can be communicated using the signals already mentioned, but often you'd want to have a word with each other. The leader will then point to a specific person, then pat the top of his helmet with one hand meaning "You, come to me". There is an issue with this signal in that other paddling cultures use the signal with different meanings. Rafters use the helmet pat to mean "I am OK", American paddlers to ask the question "Are you OK?" so this is one to check before putting on to ensure everyone takes the same meaning from it.
Once you've got your safety people where you want them, you can bring folk down one at a time. No-one moves until signalled, so if the leader's attention is taken in watching a rescue downstream, he won't find someone else deciding that enough time has elapsed and paddling on down. Once enough people are down that it seems the rapid is going well or there's enough safety boaters at the bottom, that single arm help up and now pumped up and down means "OK, everyone pile on down". That doesn't mean start a boater-cross - leave a reasonable amount of space to allow for those ahead going at a different speed or taking a different line.
"Eddy out", "Left", "Right", "Come to Me", "One person" and "Everyone flush" cover most situations, but there are a variety of signals which are useful if you are close enough to see them. One hand held up with two fingers pointing to one's own eyes means "eyeball" and indicates that the person giving the signal is going to have a look before giving further signals. If the signal is preceded by a finger pointing at you, it suggests that you should have a look. A hand held pointing downwards, waggling two fingers indicates "walk" - either get out the boat for a look, or portage round an obstacle. Pointing at a person and holding a throwbag up suggests that person should position themselves somewhere with a throwbag and further pointing may indicate a good location. Mimicking breast-stroke indicates that someone is swimming, so everyone should get themselves to a safe spot unless they are in a position to assist.
If a signal is directed at a specific person, it's conventional for that person to indicate understanding by pointing at themselves and repeating the signal. If you've understood a signal and think that the person at whom it was directed has not seen or understood, repeat the signal aimed at them. It all starts to make sense fairly quickly and the only thing to watch out for is too many people trying to communicate through signals at the same time. A whistle followed by a signal is useful if you think an instruction has been misunderstood or to attract attention if you think members of the group have failed to see something important.
Groups paddling together often invent signals on the fly and you will soon pick up various caricature actions to indicate "fisherman on the left bank", "video being taken", "go left, boof and PLF", "paddle faster, I hear banjo music" or "abandon everything and scale cliff on the right"... Don't make any safety decisions on signals that could be ambiguous - grab an eddy and find out what is going on!