Remove the battery by lifting it away from the speaker and logic board area.

Take care not to drag the battery over the lower case assembly, or you may damage the speakers or flex cables.

Before installing your new battery, remove all the remaining adhesive from the MacBook's case.

Peel off larger pieces of adhesive using tweezers or gloved fingers.

Scrape away any remaining adhesive with a plastic tool, and clean the underlying areas with adhesive remover or isopropyl alcohol. Wipe in one direction, not back and forth, until all the adhesive residue is gone.

This can take quite a bit of work, so be patient.