Replacing the battery on a MacBook Unibody is an easy task.
With the case closed, place the Unibody top-side down on a flat surface.
Depress the grooved side of the access door release latch enough to grab the free end. Lift the release latch until it is vertical.
The access door should now be raised enough to lift it up and out of the Unibody.
Grab the white plastic tab and pull the battery up and out of the Unibody.