I'm making a bit of an assumption that these tend to break in the same way for everyone. This was just my experience, so I thought I'd share in case it helps anyone out.

I've heard that these cup holders are often broken, so I was excited when mine worked fine. Then I broke it installing a head unit. I leaned over from the passenger's side to do something, heard a crack, and it was stuck open. After I finished the head unit install, I took the cup holder apart to see if I could fix it and once I figured out how it works, it was easy. I made a short video to show how it is supposed to function (this was just after I put it back together).
https://www.youtube.com/watch?v=TT6_pZSLrkU

Once you have the cup holder separated from the arm rest (3 screws on the inside), it's as easy as:

1) Take off the 3 screws holding the dark plate on
2) Remove the 1 screw holding the silver retainer. That exposes the hole where the little shiny bar goes.
3) Put one end of the bar in the hole, the other in the groove
4) Reassemble.

When playing with it, I just couldn't get it to work until I put the dark plate back on. It seems to need the tension to function.