How do you go to other regions?

You unfortunately can't go to other regions in Pokémon Omega Ruby, unlike you can in Pokémon Heart Gold/Soul Silver.

HearthGold/SoulSilver were a remake of the original Gold/Silver games, also called Gen2.
Thoses games where for the GameBoy Color, and came out at the end of the GBC's life. Whilst nearing the end of G/S's development, the developers discovered a way to compress the game's data enough to add the first game map, and did so.

It was an exception, and was not planned at the start; almost an accident. When making Gen3 (Ruby/Saphirre), they figured they were better off focusing on the new map instead of trying to add one of the previous's game world. Even the scenario made a lot less nod's to the previous game than G/S did to Red/Blue.

When creating the remake, they wanted to remake the game, without making significant changes to the way it was played, and adding such a huge area would be a significant change from the "old game".

TL:DR: You can't in Ruby/Saphirre, the only gen you can do that is Gold/Silver