1) Put down your foundation.
2) Use CTRL and drag the foundation tool to remove some of the
foundation from the middle (leave at least one square of foundation
around the outside):
3) Go to the terrain levelling tool (little spade) and choose to dig down:
4) Dig down 16 clicks and level the ground. I usually put a piece
of wallpaper (with kickboard) on the inside of the foundation so I can
see how far down to go:
5) The basement should now be the same height as a regular wall.
You should now be able to add proper walls so you can divide up the
basement space into rooms, corridors, whatever. You can also add
6) To add floor tiles to the level above, start adding tiles on the
remaining foundation around the edge, then you should find the game
adds places to add more tiles.