Within your own SharePoint sites there may be places where you can self-select which groups of which you want to be a member. In those cases, there is probably a Join button or link on a page or in a menu.
Joining a Group
To join, click on Actions, then Join Group
You will then see a confirmation letting you know you have joined the group. Click OK
Leaving a Group
If you later wish to leave the group, click on the Join or leave this group link, then go to Actions, and choose Leave Group.
You will then be removed from the group.
It's all Greek 