You can get Swapdoodle from the Nintendo eShop on your 3DS/2DS. To get stickers for Swapdoodle you have to make 9 notes. To use badges in Swapdoodle you need the Nintendo Badge Arcade from the eShop. Swapdoodle uses SpotPass to send and receive notes so make sure that's on, it's good to turn on notifications too. You should also do the Doodle Lessons. Here's a video of Swapdoodle:
https://www.youtube.com/watch?v=yyWhz26gvjQ