In fallout 3 where can I find the power armor training perk

Solution 1:

This perk is acquired from Brotherhood of Steel:

After gaining permission from Elder Lyons, speak to Paladin Gunny in the Bailey (Courtyard) of the Citadel. There is no charge or other requirement for training - the screen simply fades to black as Gunny begins teaching it. Once that's done, the Lone Wanderer may use any kind of power armor, including the Enclave and the Outcast variants.

If having not asked for training on one's own, it will automatically be given at the end of The American Dream when becoming an honorary member of Lyons' Pride, however, these options appear very late in the main quest. (Wiki-Link)