The vast majority of broadsides and leaflets have no musical notation at all. At best, they include a reference to a tune above the song, for instance: 'Set to the tune of The Silver Fleet'. Unfamiliar melodies were learned by people (directly or indirectly) from the singer who sold the broadsides. During a street singer's performance, the audience could practice the chorus by singing along.
Once a broadside had been purchased and brought home, the re-reading and singing of the song could begin. Thus, the lyrics were passed down in writing, and the melodies by oral tradition. Later, the combination of lyric and melody would pass into oral tradition.
Some singers would elaborate on the melody as they deemed fit, but some would remember the melody incorrectly or find it too difficult to sing. There are also many songs that would be sung to various different melodies, for instance because the original melody was unknown or because the singer preferred a different melody.
The tradition of referring to another tune with a phrase like "set to the tune of?" is called 'contrafacture'. Nowadays, this mostly occurs at weddings and parties. Contrafacts - new lyrics set to existing melodies - have the advantage of familiarity, which allows everyone to sing along directly (as long as the melody is well-chosen).
Many of the 'familiar tunes' referred to in the collection are now no longer familiar. In some cases the melody can still be found in songbooks or other sources from the period, but even then it is often difficult to find out how the lyric should be sung exactly.