How do you get different Rotoms?

You will need to access various appliances depending on the game. In Pokémon Platinum, you needed to download the Secret Key which was only available during a limited time and in the event of you having it as one of your items in your access then you can access a hidden room in Team Galactic's Headquarters in Eterna City in which will let you switch between all of Rotom's forms.

In Pokémon HeartGold and SoulSilver, you need to put Rotom as your lead Pokémon and then take it into the elevator in Silph Co. in Saffron City and it will bring you to another room that will allow you to switch between its various forms.

In Pokémon Black and Pokémon White as well as Pokémon Black 2 and White 2, there is an area in the Route 9 Department Store that will allow your Rotom to interact with them so that it will change between its various forms.

In Pokémon X and Pokémon Y, Rotom can change between its forms through interacting with storage boxes on the second floor of Professor Sycamore's Lab.