You form a group by inviting others to group with you or by accepting a group request.
As for Group Content in Cyrodiil, not sure, outside of Alliance War activities, if there is any real reason to group other than wanting to be in a group with someone. Even then, Alliance War does not require a group to do, it just helps.
What you might be looking for is a way to join in the Alliance War and a PvP Guild would be a good way to join in with that aspect. You can group, or not, with the members of the guild.
Enjoy the game, life is what you really want to be worried about.
PakKat "Everything was going well, until I died"
Gary Gravestink "I am glad you died, I needed the help"