You need to go to your "user control panel" (the menu item is at the top)
Then you will see an option on the left "usergroups"
or click this:ucp.php?i=groups&mode=membership
You will then see a list of all the groups that you can join, click the little circle box to the side of the group you wish to join and then go to the bottom and 'join selected' should be showing with a 'submit' button next to it, click this and you will then have sent your request to join.
to see the details of the group and the current membership you can click on the description of the group and it takes you to the details.