Braces are the best way to correct the position of teeth.  
I've never had them but my brother did. He also had to have a palate expander to help shape his teeth.
Are they painful to have?  Was that palate expander painful?
he didn't seem to be in too much pain. I'd imagine it's been made to be as painless as possible since it's such a common procedure.
How long did your brother wear the braces?
It was so long ago, I don't exactly remember. At least three years because he had very crooked teeth.
My wife had to have braces on two different occasions.  Is that common?
Not quite as common as getting them the first time, but because braces can be used for so many different reasons, and for cosmetic or structural purposes, it's not completely unique either.
I see.  How does the palate expander work?  Is that in connection with the braces or is that a separate thing?
It's used to widen your jaw so your teeth will fit better. It's not physically connected to the braces but it's used at the same times as the braces to the teeth can be adjusted while the jaw is adjusted.