Agora is played using two types of email lists: public fora, for playing the game, and discussion fora. To get the full experience you really need to follow what’s being said in both types. There’s also an IRC channel for discussion, which is more optional.
You can sign up to the mailing lists using the links on Agora’s homepage. Make sure you subscribe to agora-official, agora-business, and agora-discussion. You should also subscribe to tue, just in case activity happens there.
If you don’t want to subscribe, or want to check older messages, each mailing list has a public archive as well.
Agora-official generally is only used to publish reports. Agora-business is where people perform most of their actions. When someone replies to something sent to agora-official or agora-business, they generally do so on agora-discussion. Players also use agora-discussion to post protos (ideas for new rules) and longer winded opinions/discussions about agora as a whole.
The irc is generally where more idle chat happens, and a good place to go if you need to contact a specific player in less than 24 hours.
You do things by saying that you do them to a public forum. If the rules say that you can do X, then you do it by sending a message to the mailing list saying “I do X.” It’s that simple. In fact, becomming a player is as simple as sending a message to a public forum stating “I register as a player.”
The rules are kept in two formats: the SLR, which just has the text of the rules themselves, and the FLR, which contains more contextual information. You shouldn’t feel obliged to read them yet: the best way to learn is by playing.
Just ask! The agora-discussion mailing list is the best place to find out more. Someone will be more than happy to answer your questions.