After completing the game for the first time, the game will be saved automatically and when you load your game, you'll be back in your home in Vaniville. Go downstairs and your mom will tell you that the Professor is looking for you and will have you meet him in the Lumiose Station.
Leave the house and you'll find Shauna waiting for you outside. After a brief talk, she'll ask if you want to trade any Pokemon for the young version of the starter she chose a while back.
Once done, fly to Lumiose City (North) and head to the Lumiose Station. Get there by foot or just use a cab. Enter the station and Dexio and Sina will call you out. This time, they'll upgrade your Pokedex to the National Pokedex. This will allow you to register all Pokemon.
If you've been trading actively, you'll notice that some Pokemon in your possession have “???” in their dex number and they're not counted to your Pokedex. This upgrade will fix that and allow you to see correctly how much progress you've made towards 100% Pokedex completion.
Talk to the Professor and give you a TMV Pass which will give you access to Kiloude City
. You're probably itching to go there but stay put and check out the other stuff.
While in the city, you can fully enjoy the facilities and have access to the higher-ranked battle dining restaurants that you don't have access before. Here are some of the activities you can do:
The Battle Institute
, right beside the Lumiose Station is now accessible for you. You can now try using the Battle Tests feature.
Head to the Pokemon Lab in South Boulevard and go to the second floor. Talk to the scientist in front of the Pokeball machine to the right to receive a Poke Radar.
This is a daily event, as he will tell you about the target Pokemon for the day is. To know how to use it, please follow this link
Head to Cafe Soleil
and you'll find Diantha there. She'll trade her Ralts to any Pokemon you have. You may have a full grown Gardevoir or Gallade but Diantha's Ralts isn't half bad either. The best thing is, it's carrying a Gardevoirite