Your iMac has a Mini-DVI port at the back to connect a second monitor.
Depending upon which Display you settle on you will need either a *Mini-DVI to DVI adaptor* or a *Mini-DVI to VGA adaptor* -
http://store.apple.com/us/browse/home/shopmac/macaccessories/cables?mco=MTI2MjY
Any monitor you get will come with its own signal cable. The adaptor fits between the iMac and the Display's signal cable (i.e. iMac - adaptor - signal cable - display).
When you connect it all up and boot up the iMac, the second display will be detected automatically. You then need to go into +System Preferences/Displays+ where you will find a new option has appeared called
'Arrangement'. Open 'Arrangement' to -
a) *deselect 'Mirror'* if you want an +extended desktop+ (unlikely you will want the same display on both screens unless you do a lot of presentations), and
b) drag the diagram representing your second display to a position in relation to your iMac's own screen to match the actual physical position of your second display. (my second display is to the right of my iMac so the blue box representing my second display needed to be to the right of the iMac box).
A piece of cake.
Hope this helps
PS. My second screen is a different aspect ratio to the iMac display so, in Arrangment, it was easy to tell which blue rectangle represented which screen. If your new screen has the same aspect ration as your iMac screen they will look the same. I suspect the blue rectangle that represents your new second display will initially be the right hand one (just guessing though). You will soon work out which is which however.
PPS. Here's a suggestion (or three) for a display -
http://www.techradar.com/reviews/computing/monitors-projectors/monitors/eizo-s21 10w-48701/review
or
http://www.techradar.com/reviews/audio-visual/tvs-and-accessories/tvs/sharp-aquo s-lc32x20e-256594/specification#
and of course
http://www.techradar.com/reviews/computing/monitors-projectors/monitors/apple-23 -inch-cinema-display-225702/review