Instructions
Travel to Rustboro City and defeat Roxanne, the first Pokemon gym trainer, to receive the Stone Badge.
Complete the Devon Corporation tasks after you receive the first gym badge. Go to Steven in Dewford Town to deliver the letter that the Devon researcher's boss gives you. In return, you will get the PokeNav.
Obtain the next four Pokemon badges by defeating their respective Pokemon gym leaders: Brawly in Dewford Town for the Knuckle Badge; Wattson in Mauville City for the Dynamo Badge; Flannery in Lavaridge Town for the Heat Badge; and Norman in Petalburg City for the Balance Badge. Once you have defeated five trainers, they can start contacting you on your PokeNav.
Continue to defeat trainers throughout the game. Trainers you have beaten will contact you via the PokeNav to seek a rematch. You will receive an alert when someone contacts you. Travel back over the routes where you encountered the trainers to increase the probability of them contacting you for a rematch.
Open your PokeNav by selecting it from the main menu. You should see the main PokeNav menu, which includes Map, Condition and Trainers Eyes. Scroll down to Trainers Eyes and select it to bring up a list of the trainers you've battled. The ones who are ready for a rematch will have a white-and-red box next to their name.