Store it: Keep avocados at room temperature to ripen, and once they are ripe, refrigerate them.
Cut avocados: Leave the stone in, wrap them tightly in beeswax wrap and store them in the fridge. Placing them in an air-tight container also works well.
Freeze it: Cut in half, peel and put in a sealable freezer bag or container and freeze. Or mash or puree the flesh with a little lemon juice and then freeze in a small container, bag or ice cube tray.
Tip: If you want them to ripen them faster, place them in a paper bag with an apple or banana.