Preparation
Beacons require a CR2032 battery. These can be bought online on Amazon, or can be found in a variety of retailers.
The positive side of the battery is smooth, flat, and has a β+β somewhere on the side.
The negative side of the battery has dimples, and is slightly concave.
Replacement
Open the beacon casing by identifying the small gap on the side of the casing. Use something thin like a key to separate the 2 sides of the casing.
Remove the old battery from the beacon casing
Insert the new battery into the casing, with the positive side facing up. The beacon should flash a blue light rapidly.
Close the beacon casing by pressing the 2 sides of the casing together until it clicks. Make sure to line up the triangle eyelets.