There are multiple ways to accomplish sharing a set with others. Namely, you can email the set list, export it to Dropbox, or even Beam it.
To email: In OnSong > Select set you want to share > Tap Share Menu > Email > OnSong Archive > Send.
To export: In OnSong > Select set you want to share > Tap Share Menu > Export > OnSong Archive > Export.
For both email and exporting, when you get to the formatting screen, tap the wrench icon and select "As a single file". This will allow you to import the setlist as a whole instead of individually.