I'm playing Pokemon Y and recently, while using the PSS, I saw someone with a white sign on their avatar. When I selected him, it automatically prompted me for battle. I wanna know how to do that. Does anyone?
This should do the trick.
In the first PSS menu you have this page:
If you tap Battle you open a new menu where you can choose what kind of battle you want: Infrared, Local and Internet. If you choose "Internet" and select which battle options you like, you have to choose who you want to challenge. At the bottom of the screen, there's a button that lets you invite Friends and Acquaintance. Then, the game will automatically search for a challenger.
Probably for a friend or an acquaintance this "search" will have the look of a special icon on your avatar. I can't figure out any other process.