The basics: Using any camera, take the same shot a number of times, changing the EV each time. Make sure the range of EV values you use covers the extremes of the scene you are photographing.
You're FAR better off using RAW files, and taking at least 6 photographs.
E.g. Range of EV for scene is around -2 to ~1; take the following: -2 EV, -1⅓ EV, -⅔ EV, 0 EV, +⅔ EV, 1⅓ EV
You can also take the same picture a number of times to reduce noise. For example, take a huge number at a long exposure and you can make night look like day.
Alternatively, vary the focus instead of the EV for Depth of Field Stacking (DoF Stacking).
You're best off using a short timer (2 seconds) to stop wobbling, or a remote. If you've got CHDK then there are plenty of scripts out there, but make sure it works on your camera; I'm planning on writing one for the Canon SX200IS soon.
Thrown together by (Frag). I'm still getting the hang of this, so please feel free to make any corrections.