Whenever working near the logic board, it is always wise to first disconnect the battery to avoid short circuits.

If present, grab the plastic tab attached to the battery connector and pull it toward the front edge of the device. For Late-2011 models the battery connector will not have a tab and is simply a plug that inserts straight down into the motherboard--to remove pry the plug straight up.

If the plastic tab is missing, use a spudger to pry the connector up from its socket.

Pull the tab parallel to the face of the logic board.