In the following set of pictures, I show how I installed the window seat cabinet I built earlier...
Here is the bump-out we added for the window seat. It has a concrete floor and foundation (same as the rest of the basement) and standard framed walls.
The cabinet will be hung by the walls in the back and on the sides, and sit on the floor in the front. Here I attached 3/4" plywood pieces to the bottom to bring the cabinet up to the correct height.
Also note that I ran 3/4" boards across the bottom in the center. This was probably not needed - there won't be anything too heavy stored in this. Adding the scrap pieces took no time or cost, and it ensures there will never be sag in the bottom.
Because the wood supports will sit on the concrete, I added a layer of asphalt shingle (poly glued and stapled) to block any moisture that would migrate up into the wood over time. These get poly glued to the concrete once in place.
I build the cabinet approximately 1/2" less deep and 3/4" narrower than the opening. Just like a door, you need the rough-in dimensions to allow for some room to adjust everything. Here I added 1/2" plywood pads across the back and 3/8" ones on the right side. After marking the level-line around the walls, I quickly stapled these in place, and then firmly attached them with 2" screws into the studs.
I set the cabinet in place, pushing it against the back and right side. Once it was level and tight, I quickly shot in 3 finish nails to hold it in place. After that I drilled and secured it with 3" screws into the surrounding studs. Finally, I slid a shim in the left side and put screws in.
Here is the final photo of the cabinet in place. Note that I did not put any insulation between the bottom of the cabinet and the concrete floor. My main reason is to not allow any moisture to get trapped in there and cause problems later. I figure with the cabinet (most likely filled with blankets) and a 4" cushion on top, there will be plenty of insulation.
The next steps are to trim the cabinet to the wall and fit the lid in place. Before I do that, my DW will paint the walls, so she doesn't need to cut it in later.