To remove a contact from a group first location your contact, usually via a search. Then, using the blue links at the top find the Groups link. Select that link.
Check the box beside the group you want to remove from the contact and use the Actions Dropdown to select remove. Then click OK on the next popup.
Option 2: From the Group list
Once on RescueGroups.org go to Contacts > Groups then select the list you want to remove members from. Click on the Number next to that group. This will pull up a page with members of that group. Check the box beside the contact you want to remove and use the Actions Dropdown to select remove. Then click OK on the next popup.