I have an iMac from 2011 and there is already one external monitor connected via minidisplay port to dvi adapter. Today I wanted to connect another one, as the iMac features 2 minidisplay/thunderbolt ports. I bought a second adapter and hoped it would work just as easy – plug in and done. But the screen of that monitor stayed black, nothing happened at all. Do I need another adapter? Some additional software?
I believe you would like to take a look at this Endgadget link that explains (even with a video) what you need.
If you have two Thunderbolt ports (only the 27inch iMac), then those can support two external displays (confirmed by Apple, you can google that).
(this has been also asked on SuperUser)