Matt, pretty much what the others have said ( although I used 1-1/2 thk Blue Styrofoam instead).
You'll need to build a subfloor as well for finishing that part of the project. These came out a few years ago and can be bought at Home Depot/Lowes http://www.househacker.com/permanent/DR ... ile-System
. That said....I wish to hell they had these 20 yrs ago, I built mine by securing 1x2's to the floor in a grid pattern with a Hilty-gun then 3/8 plywood followed by the flooring of your choice. Back in the day it was all carpet but 6 years ago I tore it up and put down Laminate in the Media/Play areas and hallway.
I installed sectional Carpet (http://www.homedepot.com/webapp/wcs/sto ... idid299284
) in the master bedroom.
This is a simple DYI carpet system that I highly recommend, easy install and if you get a stain......pull the section out and slap in a new one..wa la.
All this ensures that your basement dwelling will toasty warm all winter long, we spend 40% of our time in ours.