using both monitors at once is super easy, you just plug the second monitor in and it should work straight away. If it doesn't you need only go to system prefs>displays and enable it.
when a second monitor is plugged in a tab appears in the middle of the 'displays' pane, I think (trying to remember!) with extra options for dual screens. The box 'mirror main display' is important. If it is checked the second display will simply mirror the main, unchecked it will act like 2 seperate monitors. you can also choose where on the desktop the 2nd monitor 'sits' ie to the left, to the right etc.
as for using your macbook as a computer in 'clamshell' mode, it's do able to.
heres a link
http://forums.macrumors.com/archive/.../t-213420.html
they mention a few things to be aware of, ie the heat not escaping as easily with the case closed, and the importance of giving it an air every now and then. Ie be wary of working all day with cpu intensive tasks with the macbook tucked away with no ventilation and the lid closed.
As mentioned on that forum, though, the macbook pro was designed to run like this so if anything DOES go wrong it should be covered under warranty!
edit - oh yeah, the power chord needs to be in for it to work, otherwise it will go to sleep as you described, do you have it plugged in?