Wait until evening or nighttime and use the Pokemon Hidden Machine (HM) move "Fly" to travel swiftly to Eternia City.
Rotom, Pokemon No. 479 in the National Pokedex, is an Electric-type Pokemon with a Ghost subtype. Rotom was introduced in the fourth generation of Pokemon games by Nintendo and can be found in "Pokemon Diamond" and "Pokemon Pearl." You will need to get data for Rotom, which can only be gained by capturing it in the wild, in order to complete your Pokedex.
Exit the city through the Eastern gate in the Northeast corner of the town.
Walk to the left and find a row of sapling trees in some bushes. These trees can be removed with the HM move "Cut." Cut down the trees and head North into the Old Chateau.
Go up the stairs to the second floor and enter the room with the television. Walk up to the TV and press the "A" button to interact with it. Rotom will appear and battle you.