How do anonymous hackers communicate with each other and keep their communication secure?

There are many ways off doing this, but I discuss two here.

1. An older method is using an old protocol called internet relay chat, or IRC. The hacker puts a small program on yhe victims machine. The program listens for commands given in a IRC chat room by the hacker. Because of the way IRC is programmed it is difficult for any third party to determine which rooms are populated by whom, and they can be pass word protected. The hacker will ping off of several proxies (typically using encrypted ssh), join the chat room, and give commands to the bots on the infected machines.
2. TOR or similar onion routing protocols allow a persons traffic to be anonymously routed from random locations making it nearly impossible to determine the origin of the traffic.

In most cases, hackers combine the above two to allow them to correspond with others on infected computers.

Download TOR here