All group members will be able to leave the group they are a member of. Below are the steps to leave a group:
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1. All the groups accessible to you will be available to search from within the left panel. Upon mouse hover on a particular group and clicking on icon, you will get the available options for that group.

2. Click on the 'Leave' option to leave selected group. A message will appear on the screen confirming that you have left selected group. The group administrators can still add such users again to the group.
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In case there are any incomplete tasks for you on the selected group, you won't be allowed to leave a group without reassigning them to some other user.
In case you are the only administrator in selected group, you will be required to assign another administrator to the group before leaving it.
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Alternately, you will also be able to leave a group while viewing a group by clicking on 'Leave Group' link:

3. Once you have left a group, that particular group won't be accessible for you (until group administrator adds you back).