I absolutely love this glitch, and I use it to flash around some impressive Pokemon. This is a party I made using it (and also the Celebi glitch, but that's for a later time):
These instructions are how to make any captured non-shiny Pokemon into a shiny one on Pokemon Crystal.
First, you need a shiny Pokemon. Any will do. I started out making shiny Pokemon with one from the mysterious egg I got from the day-care center, which happened to hatch shiny for me, but in this tutorial I will be using a shiny Ditto.
Second, choose the Pokemon you would like to make into a shiny. Electrode is my choice.
Third, you'll need a damper Pokemon so you can deposit both the shiny Pokemon and the non-shiny Pokemon (anything will do, I'll be using my Lugia)
(This is my party)
Now onto the meat of the tutorial.
Position your Pokemon in your party like so: Non-shiny, shiny, damper.
Now to start with the glitch. Save the game, then choose an empty box, (mine will be Box 8). Into this box, deposit your non-shiny Pokemon and your shiny Pokemon.
Now select "Change box" and press A. Select any box, and when it asks to save the game, select "Yes" and "Yes" again. Right after the period on the message, "Saving, don't turn off the power." turn off the power. Turn the game back on, and if you did it correctly, there should be your non-shiny and shiny both in the PC and in your party. Congratulations, you've successfully cloned Pokemon.
However cool that was, it isn't the end product we're looking for. Withdraw the two Pokemon from the PC and make your party follow this suit: Non-shiny, shiny, non-shiny, shiny, damper.
Save your game, and prepare yourself for some more cloning. Deposit all 4 of your Pokemon once again, and follow the cloning process I taught you in the last step until there are 16 Pokemon in the box, and 4 in your party (not including the damper).
At this point, deposit a non-shiny and a shiny and save your game. Now deposit your last two, and clone them. You should now have 20 alternating (non, shiny, non, shiny, non, ect...) Pokemon in the box, and 3 in your party (non, shiny, damper).
You are now ready for the final (and most difficult) step.
Withdraw the first Pokemon in the box, and immediately deposit it back into the box. [if your non-shiny Pokemon was first, the box should now start with a shiny, and alternate the same way as before (shiny, non-shiny, shiny, ect...)]
Select "Change Box" and follow the cloning step processes, but this time, you need much more precise timing for shutting off the game. Immediately after you see the period, shut off the game. Turn it back on, and check the box. If the nicknames are changed to the other Pokemon's name, you have done it correctly, if not you must try again. Simply withdraw the first Pokemon again, and deposit it once more, follow the cloning process again. Patience is key here.
Once you've done it correctly, look through all of the Pokemon. Many of them will have different sprites, but actually be the original shiny Pokemon (such as the following: I got sprites of a shiny Electrode, but in the stats screen, it said Ditto/Ditto) this isn't what we're looking for. Look in the stats screen for the one that says [shiny Pokemon name]/[non-shiny Pokemon name] (obviously, replace the bracketed objects with your Pokemon's name) and has a shiny sprite of the Pokemon you were trying to make shiny.
[On occasion, this Pokemon isn't there. You'll have to release all the Pokemon in the box and start over. It sucks, but I've had it happen to me before. This glitch is the reason I keep the two originals in my party at all times.]
Withdraw this Pokemon, and take them to the Name Rater in Goldenrod. Rename them whatever you want and CONGRATULATIONS. You just made a shiny Pokemon!