How do I get Power Armor training in Fallout New Vegas?

Power Armor Training in FO:NV is available at the end of a few different quest chains in order to provide access for a variety of paths.

From the Brotherhood: After completing Eyesight to the Blind or Still in the Dark, wait 24 hours for the lockdown to end, and the Elder will offer you PA:Training, whether McNamara, or Hardin. (Hardin may ask you to go blow up the Silver Rush before offering training.)

Alternately, you can complete Arcade Gannon's follower quest, For Auld Lang Syne - in addition to rewarding you with the unique Tesla Power Armor, you'll receive the necessary training to use it.

After the lockdown is complete the elder will give you a quest called "Eyesight in the Dark". Complete this mission and earn your place amongst the Brotherhood of Steel. Oh, and for the record, you dont have to side with Hardin. I ignored Hardin for the most part. I told him i'd see what i could do but then never interviewed the other Paladins until after the mission for the components was finished and then i only interviewed one of them. I waited like 6 days before the lockdown was over and nothing. Then I zoned out to LT 1 and then zoned back in and voilà. Hope this helps.