After you go through Route 101 and explore Oldale Town, go north to Route 103, where your rival awaits.
Go through the Route
Go north, then east and north through the grass. After that, go west to the next patch of grass and go west and north through it. At the north part of the route, you can see your rival standing in a patch of grass. You can use a potion to heal your pokémon's HP. When you're ready, talk to your rival.
If you choose Treecko, your rival will have a level 5 Torchic. If you chose Torchic, your rival will have a level 5 Mudkip. If you choose Mudkip, your rival will have a level 5 Treecko. Your rival chose the type of pokémon that is strong against yours, so only use your Normal-type attack during this battle. In other words, if you have a Treecko that is level 6 or higher, don't use Absorb, or if you have a Mudkip that is level 10 or higher, don't use Water Gun, or if you have a Torchic that is level 10 or higher, don't use Ember.
Return to the Lab
After the battle, go south by jumping down the ledges until you are back in Oldale Town. Heal up and buy supplies at the Pokémon Mart if you want to, then go south through Route 101 and go back to Littleroot Town. Go into the Lab. You will automatically go up and talk to Professor Birch. He gives you your Pokédex, which allows you to record details of the pokémon you encounter. Pokémon that you see but don't capture are added to the Pokédex automatically, and their details are filled in if you capture them.
Afterward, Brendan gives you five Poké Balls. You can use them to catch pokémon.
Get the Running Shoes
Leave the lab and go north. You will see your Mom standing outside. Talk to her. She says a few words, then gives you the Running Shoes. You can hold the B button to run. But be careful: if you run through the grass, you might encounter more pokémon than usual.
Catch Some Pokémon
To catch pokémon, just walk in the grass or other areas where you encounter pokémon, then when you encounter a pokémon, open your bag and use a Poké Ball.
However, to improve the chance that the Poké Ball will capture the pokémon, try reducing the pokémon's HP as much as possible before you throw the Poké Ball. Also, later you will be able to cause status conditions like sleep, freeze, poison, burn, and paralysis. A pokémon with one of these conditions is easier to catch. Poison, Burn, and Paralysis only improve the chance a little bit. Sleep and Freeze improve the chance the most.
In Route 101, you can catch Poochyena, Zigzagoon, and Wurmple. In Route 103, you can catch Poochyena, Zigzagoon, and Wingull.
You can buy more Poké Balls in Poké Marts.
Continue Your Adventure
After you catch some pokémon, go back to Oldale Town, then go west to Route 102.