The iconic Power Armor in Fallout 4 is powered by fusion cores. These energy cells can be found in many locations throughout the Commonwealth. However, finding a sufficient number can be tough.
You can pickpocket them from NPCs, take them from powered machinery, find them on enemy corpses or buy them from merchants who sell weapons and ammunition. While these are all viable options, the best way to get a hold of them is by scavenging for them in the Wasteland.
Some of the best places to scavenge for Fusion Cores in the game are below:
The Sludge Works
In Appalachia's Ash Heap region, there is an abandoned mineshaft near Rollin's Work Camp where you can find a fusion core tucked inside a basket in the basement. There are also several of them tucked into storage rooms at the Big Bend Tunnel in the Cranberry Bog, as well as a few at Fort Defiance.
In the Roadside Pines motel, a generator in the back of the building houses one of them. The crate next to the sentry bot can also contain a core, and there are two more at the Robotics Disposal Ground.
In Sanctuary, there is a facility with a fusion core that is full of radiation. This is a challenging location, and you'll need to avoid the Feral Ghouls that populate it as well. Fortunately, there is a door in the basement where you can hack a computer to gain access to it.