I just started playing Omega Ruby and it has been years since I've played.
After I catch a pokemon that goes into my pokedex, how to I transfer it into my lineup so I can use it in battles?
You have a couple of options that can happen:
If you have less than 6 Pokemon in your party, any captured Pokemon will automatically be added into your party.
If you have 6 Pokemon in your party, any captured Pokemon will be transferred to your PC. You can access your PC at any Pokemon Center.
If the Pokemon is automatically added to your party, you will need to take them to the Pokemon Center to heal them. Pokemon taken out of the PC are already fully healed