Yes, me pongo de pie almost translates to "I put
myself on foot", of course, literal translation to english sounds a
little bit funny, but indeed it means "I stand (on my feet)".
So the me pongo here means...I put myself..."up" or "on my
feet" or "standing" hehehe....I know you get the idea!.
Ponte en mi lugar or me pongo en tu
lugar are other phrases that use poner and
they mean, "put yourself in my place/position" and "I put myself in
your place/position"...or as we also say ...en mis zapatos (in
my shoes) .You might use it as "walk a
mile in my shoes"...