Instructions
Locate a town with a Pokemon Center. You may walk or fly to the nearest one, as most towns are equipped with one. Enter the Pokemon Center and open the PC located on the right of the building by standing in front of the computer and pressing the "A" button.
This will open the user mail and Pokemon storage system prompt. Select "Bill's PC." Deposit the Pokemon you wish to clone and place it into a storage box. If the Pokemon you want to clone is already in storage, disregard this step. Either way, save your game once you have the desired Pokemon in the computer.
Turn on the computer again. Enter "Bill's PC" and move the selected Pokemon to be cloned to another (different) box. You will be prompted to save the game while the Pokemon is being transferred between boxes. Go ahead an accept. When the "Saving... don't turn off the power" message appears, immediately turn off the Gameboy.
Turn on your Gameboy, and enter the saved game again by selecting "Continue" at the game selection screen. Check the boxes where the Pokemon to be cloned was originally placed, as well as the box where it was supposed to be transferred. You should now see them in both, and the cloning is complete.