The Heirarchy of Smooth Tracking Shots
When you want to get a shot of someone or something moving from point A to point B, you'll want to move or "track" with them. There are several ways to do this, most of which depend on how much you want to spend and/or how skilled you are. Sometimes you want a very smooth move and others you want to be jerking all over the place. The following is the short list of the basic devices you can use to achieve these effects, and how you might be able to get away with a clone of that device.
The Camera Dolly - Essentially a board on wheels. You mount your camera on the board and roll with your shot. A filmmaking mainstay, nothing beats a well-executed dolly shot. The best dollys are heavy with solid steel track that has to be set up properly. There are many DIY dollies out there, typically made of skateboard wheels and PVC pipe.
The Stedicam - First used in Rocky when Sly ran up the steps in Philly, the Stedicam (and it's imitators) is a balanced system that "floats" on a centralized gimbal. Tough to use (much practice is required), but can be of great value when you can't lay track or don't want it to be seen. Sometimes called a "dolly that bleeds". There many homemade versions out there, but smoothness is still dependent on the time you want to put in.
The FigRig - Developed by director Mike Figgis this thing looks like a steering wheel with a camera in the center. Credit should also go to Sam Raimi and the Coens who used a similar gadget called the "shakicam", which was a camera placed in the center of a 2x4 and held on both ends. Using your arms as a smoothing device, you can get some pretty good shots with this gizmo and cloning it for cheap is easy.
Handheld - The easiest way to track is to simply hold the camera with your hand and follow the action. It also looks the cheapest, but can come in handy when shooting docs or wanting to create an uneasy universe.
Which ever method you pick, you really can't go wrong by figuring some way to work the tracking shot into your project. They are really that useful.