The easiest way to scan songs directly into OnSong is to utilize OnSong's Document Scanner, which is an OnSong Premium feature.
Additionally, if you go into the Notes app > iCloud > Notes > Select a new note > Tap the "+" sign that in a circle > Scan Documents > Take a picture > Adjust how you would like the perimeter > You can then either retake the picture or keep scan > You can then either keep scanning or Save. > Tap the scan > Tap the Share Icon (square icon with an arrow sticking out the top) > Save to Dropbox or a similar storage provider since it will not let you save it directly to OnSong. Once saved in Dropbox though, you can import them into OnSong.
However, there is a scanner app called Scanner Pro by Readdle that also works well. You can then directly import the content from the app into OnSong. We believe this app is currently $3.99 or so on the App Store.