After receiving data from another player, that player’s Shadow Link will appear somewhere in the game world. Seek out the Shadow Link and you can fight him–win to earn the bounty of rupees on his head. The higher the bounty, the tougher the Shadow Link.
To set up StreetPass, speak to Gramps who’s standing in an empty field on the left side of Kakariko Village and choose “Setup” from the menu. The following screen will show Link’s heart count and equipment; what you see here is what other people will see when they fight your Shadow Link. At this point, you can opt to change Link’s items; by default, the items he’ll have will be the ones currently equipped to the X and Y buttons. When you’re ready, go to “OK” to send out your Shadow Link; you can also change the settings afterwards.
Note that your Shadow Link isn’t automatically updated as you play–you will need to speak to Gramps and choose “Setup” again to update.