After passing through Oldale Town, you should continue north to Route 103 to meet up with your neighbor.
Go Through the Route
In the route, go east and walk through the grass to get around the ledge to the north. There is some water to the east, but you can't get past it. Go north and you will find your neighbor in the grass.
Battle Your Neighbor
Your neighbor challenges you to a battle. If you chose Treecko, your neighbor chose Torchic. If you chose Torchic, your neighbor chose Mudkip. If you chose Mudkip, your neighbor chose Treecko.
This means that your pokémon will have a type disadvantage to your neighbor's pokémon, so don't use a move that matches your pokémon's type, because that move will be weak against your neighbor's pokémon. Instead, use a normal attack move.
Go Back to Littleroot
After the battle, your neighbor heals up both of your pokémon, then returns to the pokémon lab in Littleroot Town. You should go there, too. You can jump down the ledges to avoid the grass. Go south through Oldale Town. Your neighbor will meet you just before you enter Route 101 and remind you to go to the pokémon lab. Go south into Littleroot Town and enter the pokémon lab in the south of town.
Receive Your Pokédex
In the pokémon lab, Professor Birch gives you your very own pokédex. Your neighbor gives you ten poké balls. Now you are ready to go on your pokémon adventure!
Now that you have a pokédex, you can use Pokémon Bank (available from the 3DS eShop) to transfer pokémon from Pokémon X and Y into your game. If you download Pokémon Bank from the eShop, you can go to the Pokémon Bank main menu and download Pokémon Transfer for free. You can then use Pokémon Transfer to send pokémon from Pokémon Black, White, Black 2, or White 2 to your Pokémon Bank, and from there you can send them to Omega Ruby or Alpha Sapphire. For more information about trading pokémon, visit the pokémon trading instructions page.
Get the DexNav
When you go north from Littleroot Town, your Mom stops you and tells you some words of encouragement. Then when you go farther north and enter Route 101, your neighbor stops you and gives you an upgrade for your PokéNav Plus that Professor Birch forgot to give you. The upgrade adds the DexNav to your PokéNav Plus.
The DexNav is a very helpful tool that tells you which pokémon can be caught in a particular area. After you catch a pokémon of a certain type, you can tap that pokémon in the DexNav to search for other pokémon of that type nearby. Not only that, but the more you encounter that type of pokémon, the better the DexNav gets at searching for it. You can even find pokémon that have rare moves and hidden abilities with the DexNav.
To switch to the DexNav, tap the DexNav tab on the right (with the Pikachu on it) to see a view of the current area. Tap on the area to see a message about how close you are to catching all the types of pokémon available in this area. Once you have caught all of the types of pokémon in this area, the DexNav will display a crown in the top right corner.
Be sure to spend some time running around in the tall grass of Route 101 to catch pokémon. You can find Wurmple, Poochyena, and Zigzagoon in this area.
To catch pokémon, you have to throw a pokéball at a wild pokémon. But the pokéball works best if the pokémon that you throw it at has been weakened. Try to reduce the pokémon's HP as much as possible before throwing the pokéball. You can also try to inflict status conditions on the pokémon if you can. Making a pokémon fall asleep increases your chance of catching the pokémon a lot. Freezing the pokémon also works well. You can also poison, burn, or paralyze the pokémon. This doesn't improve your chance as much as sleep or freeze, but it does help.
Go north through the route and you will find your neighbor again. Your neighbor will notice a pokémon hiding in the grass and will teach you how to sneak up on it. When you get close enough, the battle will begin. Weaken the pokémon as explained above, then throw a pokéball.
You can also go up to Route 103, where you first battled your neighbor. You can catch Wingull, Zigzagoon, and Poochyena there.
When you're ready, go to Oldale Town and use the west exit. You will reach Route 102.