Each group has a link "leave group". To leave facebook group you can follow bellow steps;
Step1: First, log in to your personal Facebook account click Home tab.
Step2: In the lefthand sidebar click “Groups.” (If you don’t see the “Groups” tab, click the “More” link and it will display hidden tabs. A list of all your groups will display in the middle of your screen.
Step3: You can see a pen icon (like
) left of the group name.
Step4: Click the pen icon. Facebook will prompt you, “Are you sure you want to leave this group?”
Step5: Click “Leave Group” button (Or click “Cancel” if you have second thoughts and really don’t want to remove yourself from the group.)
Step1: First, log in to your personal Facebook account click Home tab.
Step2: In the lefthand sidebar click “Groups.” (If you don’t see the “Groups” tab, click the “More” link and it will display hidden tabs. A list of all your groups will display in the middle of your screen.

Step4: Click the pen icon. Facebook will prompt you, “Are you sure you want to leave this group?”
Step5: Click “Leave Group” button (Or click “Cancel” if you have second thoughts and really don’t want to remove yourself from the group.)
You are now leave from the Facebook Group.