For starters, this thread seems laden with good advice, as does this one.
My experience with greenscreening is purely with live action, so some of this might not be applicable to the much smaller scale used in brickfilming. Hopefully the experienced brickfilmers will call me out on any false information.
Green posterboard seems to be a popular choice for the background, but paper, cloth, or anything else that is a uniform color that isn't the same as anything in your scene will work. Once you've got that, make sure your subject is a good distance away from the greenscreen. If your subject is too close, there's a good chance (especially with LEGO) that light will reflect off your background and create an ugly green halo around your subject that's extremely difficult to get rid of.
You need a minimum of two light sources, preferably three or more, to green screen properly. Use two lamps, one on each side of the green screen, to light it evenly the whole way across. Make sure you prevent the light from shining back onto your foreground subject and creating shadows. If you're greenscreening the floor as well, don't have a sharp crease where the wall meets the floor, as this will create a much darker green in the corner, making it difficult to key out without the use of a heavy duty program such as After Effects. Curve the joint instead.
If ambient light isn't enough, use a third light to light your subject. Make sure you diffuse this light if necessary to prevent it from creating a shadow on your background. In case you haven't noticed by now, shadows are your enemy--they create darker shades of green that make it much more difficult to pull a good key. This diagram shows the setup for the first three lights.
You can also help get a clean edge on your subject by using a reflector--a white index card should work well--to put some light onto the rear of your subject. In effect, this creates a tiny, faint halo of light around your subject. If you do it right, the effect will be barely noticeable on camera, but it will make it far easier for the computer to determine where the edge is.
Hope this helps.
With all due respect Noodle, I don't want you here. - Ratboy Productions