So I was watching the combat showcase on Bethesda's official youtube channel, and it showed the player talking to Garvey, and about clearing out Raiders. It then led to the scene of powering up the Power Armor, and a brief flash of a mission update about clearing out the Concord.
During the footage, which seems heavily scripted, it's evident that the Power Armor takes a heavy beating, parts breaking off of it.
I think this is how we acquire it first. We find it and power it up during this story mission of clearing out this army of raiders, and during that battle, and the following battle with a [censored]ing Deathclaw leaves it in the state of repair that we see in the garage scene, and in the demo footage.
Does this explain how and why we know how to operate Power Armor? No, not enough evidence. But I'd put caps on the dime that this is how we get ahold of our ol' ironsides. It's not given to us, we just happen upon it, and utilize it for the situation at hand, and boom...well, she's busted up, but we can fix her.
Edit:
Further considering HOW we get it piloted...I imagine it becomes a side quest within the quest. There's heavy ordinance in that busted up ship there. Oh crap I have no idea how this works. Hunt down a US Army Power Armor Users Manual and a power core or whatever that thing is, boom.