To activate StreetPass for the 3DS Sound app, tap on the StreetPass button on the lower left of the touch screen. The lower part of the screen will have a button that says StreetPass Off. Tap that to turn StreetPass on.
This requires that you have at least one song in the StreetPass playlist. To achieve this, first you must put a song on your SD card from another device, such as a computer. To do this, insert your SD card into an SD card slot if your computer has one or a card reader peripheral reader otherwise. Then the SD card should appear as a drive in your computer, and you can copy files to it the same way you can with a flash drive or generally moving files around in your file system browser. The music files have to be of one of these four formats: .mp3, .m4a, .mp4, or .3gp and they have to be in a folder.
Then put the SD card back in the 3DS and open the Sound app. In the app, navigate through the folders to a song and select it. There will be a button on the bottom right that says Add..., which you can click to add the song to a playlist. Once you add a song to the StreetPass playlist, the option to activate StreetPass will become available.