Powering options can vary from monitor to monitor. Sometimes monitors come with an option to run on AA batteries (but not always).
On-camera monitors often need to be powered by external rechargeable camera batteries, like the Panasonic CGA-D54 battery (or more affordable third-party versions of these batteries). Sometimes on-camera monitors will come with battery plates for a number of different batteries, other times the plates need to be purchased separately.
It’s also fairly common for monitors to feature external power inputs, for either AC adapters or battery distribution systems.