Here's how to. First of all, you must have already "unlocked" Battle Frontier, by beating the Elite 4. Afterwards, fly there and find the Battle Tower. Now, before you can clone your Pokemon, you need to already have it in your party. Go to the PC and deposit that Pokemon, exit the PC and save. Now open your PC again, and get that Pokemon you wanted to clone. Talk to the LINK MULTI BATTLE ROOM lady. Tell her CHALLENGE. Now choose the category of the Pokemon to be cloned and select two Pokemon. Now the lady will say: "Before entering BATTLE ROOM, your progress must be saved. Is that okay?" Say YES. Now you will notice a small time gap. Your Pokemon has been successfully cloned! When the text "Would you like to save the game?" appears, tell her NO. Now turn off your game, and turn it on again. You will notice the Pokemon in your party and in your PC.
Note: You can do the same way to get infinite items. Just make the pokemon cloned, hold the item.