In order to duplicate monsters, you need two unique save files. They either have to be named differently or have different Symbol attributes. Also make sure that the monster you want to duplicate is in your capsule stock.
For example, let's say you have a save file named "Player 1" and you want to duplicate a Blue-Eyes White Dragon. Put the Blue-Eyes White Dragon in your capsule stock. Then start a brand new campaign game and name it something different like "Player 2."
Now go into Versus mode and pit Player 1 against Player 2, each using their own respective save file. In the duel options under "Ante Monster" have Player 1 bet the Blue-Eyes White Dragon that was in its capsule stock. Proceed with the duel and have Player 2 beat Player 1 either the old-fashioned way, or have Player 1 surrender.
After the duel is over, have Player 2 save its game file, in order to register the newly acquired Blue-Eyes White Dragon, but do not save Player 1's save game file. Now exit to the Title Screen. Player 2 will now have a duplicate of Player 1's Blue-Eyes White Dragon.
If you want to transfer the Blue-Eyes White Dragon from Player 2 to Player 1, just repeat the steps and reverse the procedure from Player 1 to Player 2. You can duplicate as many monsters as you want this way, and it makes it easy to obtain fusions that require 3 monsters, such as Harpie Lady Sisters or the Blue-Eyes Ultimate Dragon.