I've been recording some movies of solutions to Lode Runner levels for Lode Runner On-Line: The Mad Monks' Revenge. (Most levels are identical to those in Lode Runner: The Legend Returns.)
First of all, you need to unzip the file. Use any unzip utility, such as WinZip. After unzipping, you'll have an AVI file.
To play the AVI file, you need an AVI video player (if you use Windows, Windows Media Player or almost any other video player will probably work), and an XviD decompressor (usually called a "codec"). If you use Windows, you can probably get what you need at koepi.org. For Macintosh or other OSes, I don't have any suggestions, but you can probably find something if you search the web.
I'm afraid the videos are quite small and low-quality, and have no sound. I recommend using the full-screen or double-size option of your video player, if it has one.
I basically tried to make the file size as small as I could, while having the visual quality just good enough to make out what's going on. I think I may have overdone it, though -- the monks are nearly invisible sometimes on levels that have a reddish background image.