I know it can be done, lots of people have said it. What they don't say is how! I've been looking through forums and videos, but I've only managed to use the basement tool to create a giant undergound square that is completely unaccessable.

Can anyone who's done this sort of thing before post some instructions? or better yet, a video?

Thanks in advance!

Make the basement first under the house, and then delete 4 floor tiles in a row on the lowest floor of the house, so you can place stairs down into the basement. Sometimes stair placement is fiddly with basements - just keep clicking at the end you want the stairs to stop at, and drag toward the hole made by the 4 missing tiles. Eventually the stairs should turn green and place.

Oops, I forgot to mention that the house has a foundation. So I delete enough foundation to add downwards stair, but it just lead to the grass underneath the house and not the basement. :S

Then you'll need to remove five tiles of floor and do two sections of stairs - one section that's 4 steps high down to the grass (you can always put a floor tile on the grass) and then another full-height section 16 steps high from the grass to the basement.

Ok, tried that and when I try to make the second set of stairs it says: 'terrain too high to place stairs on basement.'

There seems to be a bug concerning the height of foundations and basements: They are slightly off, apparently making it impossible to build stairs between.
What you can is the following: First, create a staircase to the basement outside the house (may need a few tries, and may need to be several squares away from the house). You should notice that the ground at the top of the stairs is a little lower than the surrounding ground. This is the height the ground needs to be where you want to place your actual stairs.
So use the cheat and level the terrain you want the actual stairs to go (under the foundation) to the height of the terrain at the top of the outside stairs. Then use .
Now you should be able to place the stairs within the foundation (for some reason it doesn't work in every position for me, so you may need find where it allows you to position the stairs).
You will need to use the constrainfloorelevation false cheat again to level the foundation of your house again to its normal height, but then everything should be fine.