I found the below video useful for explaining the principles of a steadicam, which really helped me understand how and why a steadicam works, and what needs to be taken into account when building my own.
To summarize, you need to counteract the camera's movements in 3 ways - Pan (Side to side) Tilt (Up and down) and Cant (Twist). If these 3 movements can be isolated, the whole camera's movements can be.
The ways to do this are by creating a device that allows movement in those 3 directions, a Gimbal. A gimbal is a device that allows movement in multiple directions through one point of rotation. This can be a ball-and-socket joint, or the kind of thing you see here - http://www.yb2normal.com/DIYsteadicam.html
When you have this Gimbal, a camera attached on to it, and some sort of weight to keep the camera held down, you have a basic steadicam. The idea is that the gimbal allows the shake that would be present in the camera footage to be compensated for, reducing much or what you see.
For my design I used:
A Tripod head (I had this already and it means easier mounting and greater control, but there are many other ways that you can attach your camera)
1 metre long 10mm threaded screw pole (This thread fits the thread in the tripod head)
1 metre 8mm threaded screw pole
8mm lock nuts (I think i used about 12)
10mm lock nuts (I used 4)
washers (quite a few)
a spinny bearing thing