Gone are the days of the Player Search System.. at least in Pokemon Sun/Moon. Pokemon Sun and Moon introduce a new feature called the Festival Plaza and it allows players to battle and trade over Wi-Fi. This guide shows you how to achieve the task.
How To Battle and Trade over Wi-Fi in Pokemon Sun/Moon
Step 1: Open the main menu on your game and choose “Festival Plaza”.
Step 2: Select the blue signal button to the bottom-right corner of the bottom screen on your Nintendo 3DS. This will let you connect to the Internet (if you do not connect to the Internet, obviously you can’t battle or trade over WiFi).
Step 3: Choose either the Battle or Trade buttons depending on what you wish to do (you can’t miss them, they are large and in-your-face).
Step 4: A list of players (friends and strangers) should appear on your guest list (alternatively, you can also use your VIP list). You can send battle or trade requests to them.
Select the person who you want to battle or trade and they must accept your request to continue.