When you write a new song from the Add Songs Menu, OnSong opens the Song Editor and shows you an example song to help get you started. You can remove this song by tapping into the text and tapping again to open the menu and choose "Select All". You can then either delete the text or start typing over the selected text to create your song.
To set a new default template for new songs, just do the following: Open OnSong > Tap on Songs > Tap on + > Select New Song > Delete what is there > Type in what you want your default template to look like > Tap on the Hammer Icon > Use As Template toggled to On > Close text tools by tapping on the main editor > Tap on Done to save your changes.
You can also turn off this template song completely in settings. To do this, go into the Utilities Menu by tapping on the gear icon in the Menubar and choosing Settings > Menu Settings > Song Editor > Use Template Songs, and turn that setting off. Tap Done and the next time you enter the Song Editor, you'll have a blank slate to start with.