Basics
Each Wii remote requires 2 standard alkaline AA batteries in order to function. The Nunchuck attachment does not require batteries.
Lifespan
According to IGN.com, a single pair of AA batteries will power a Wii remote for roughly 30 hours, or longer if the pointer technology is not used (see Resources).
Replacement
The battery compartment on the remote is located on the back, near the bottom (or the end furthest from the pointer mechanism). Also, Nintendo's customer service website says to "insert the minus (-) end first when inserting new batteries, and remove the plus (+) end first when replacing the batteries" (see Resources).
Rechargeable Batteries
In theory, any type of rechargeable battery can be used in a Wii remote. However, Nintendo only recommends use of Nickel Metal Hydride (NiMH) batteries.
Charging Stations
Nintendo does not currently produce an official recharging station for Wii remotes. However, several third-party manufacturers, including Intec and Nyko, do provide such products.