You can either buy Pokémon Bank, or trade them to yourself.
Pokémon Bank:
Deposit the Pokémon from Omega Ruby that you want into Pokémon Bank. Eject Omega Ruby and insert Y. Go into Pokémon Bank again and withdraw them onto your Y game.
Trading:
If you have no Pokémon Bank, but access to two 3DS systems, you can link trade Pokémon from Omega Ruby to Y. This is the optimal method if you can borrow a 3DS and do not want to pay $5.00
Please keep in mind that if the Pokémon you are trading know moves, have abilities or hold items that are not available in Y, you will not be able to send them back. For example, a Gyarados that knows Crunch in ORAS cannot migrate back to XY, because in XY Gyarados did not know Crunch.
Overall compatibility.
List of ORAS move changes.
