You will need a micro USB to MH/HDMI adapter, a HDMI compatible monitor, and a set of bluetooth keyboard and bluetooth mouse. I use the Apple keyboard and bluetooth mouse.
This will basically mirror everything you see on the phone to the monitor. If you don't have an HDMI monitor, you can use a HDMI to DVI adapter like the one I use on this 24" Samsung.
The screen res will be what is on the phone, 1280x720. Some apps don't work quite right due to the fact they require or shift from landscape to portrait mode. For example, pulling up Netflix's movie browser looks like this:
Overall, it is a silly demo to show off your friends and colleagues. Running ICS on a large monitor is not really that intuitive when you consider the oversized icons and UI elements designed for a 4.65" phone. The phone should have outputted a 1920x1080 display which would have been my preference.
Now, if this could dual boot into something like Ubuntu, then I can see the value of it. The original Atrix and their webtop was a very promising idea in 2011. Since, it the concept and execution has sort of fizzled into obscurity.
One last note, the MHL adapter requires power. You will need to use the existing micro-usb power adapter to power it. This sorts of kills the whole idea of using the Galaxy Nexus as a portable presentation machine. In comparison, the iPhone 4S and iPad 2/3 can be docked with a 30pin-HDMI adapter and run on battery alone.
LINK for MHL adapter: http://www.amazon.com/Menotek-Adapter-IMPROVED-Protocol-Sensation/dp/B005F9W6DU/ref=sr_1_3?ie=UTF8&qid=1342718283&sr=8-3&keywords=MHL+adapter+nexus