You set up "bookmarks" within TeamSpeak. Each bookmark would be for a different guild's TS server. Each server usually has several different channels within it. So, if you are running with "Guild A" for example, you would log into Guild A's TS server. Once in that server, you need to know which channel your group will be using, then you just move to that channel.
Lets say you get done with Guild A's activity, and now you are moving on to Guild B for another activity. You will then log out of Guild A's TS server, and log in to Guild B's. Then you need to find out which channel your group is using within that server and then move to it.
All of this is done within the TS interface. ESO and TeamSpeak are 2 separate, unrelated programs. They do not "work together". You cannot control game functions from TeamSpeak, and you cannot control TeamSpeak functions from ESO (or any game), as it's its own program.