After the invention of moveable type by Gutenberg, one of the earliest things he printed ( after the bible) was music, around 1465. Before this of course everything was hand copied, so quite expensive. Printing made music much more easy to distribute. But for the first couple of decades of the 16th c. it was still pretty laborious. Octavio Petrucci, who was the first to do it well ( circa 1501) had to make three impressions to do one page: one impression for the words, one for the staff lines, and one for the notes. That was eventually superseded by a one-impression method that was faster and so somewhat cheaper. The result was a lot of music began to be printed. A lot of the present repertoire of early instrumental music for consorts of recorders, winds, viols, etc is known by their publishers: Susato, Praetorious, Ballard & LeRoy, Phalese....There's plenty of iconographical evidence of the 16th c., pictures, from the period showing musicians reading from books, often gathered around a table. The music-publishing trade had to have been pretty lucrative. Queen Elizabeth I was fond of granting monopoly patents instead of giving out money, as they conferred a benefit and they didn't cost the crown anything. Instead of paying her two favorite musicians, she granted a monopoly to them, giving composers William Byrd and Thomas Tallis exclusive rights for printing music books and music ( ruled) paper for 21 years.
In the early decades of the Early Music revival, there was a general reliance on those early printed works, and a general assumption that , because all the modern musicians were working from them, most musicians of the period would have been working from them as well. But before music printing became possible there was a system of learning and memorizing music that did not require reading, a Solmisation method now generally known as the Guidonian Hand, named for Guido of Arezzo, who in the 10th c. AD. supposedly came up with the basis of the standard music notation used today It assigned a note to various places on the hand. This tied a piece of intangible information ( the name of a note) to an actual thing ( a place on the hand) and an actual pitch. (In this it was somewhat like other early memorization systems: walking down a street and reciting each stanza of a long poem before the door of each house later enabled the orator to walk down the street in her mind and recall each stanza before every door). This seems to have lasted quite a long time into the 16th c., long after a lot of music was being printed. Not only was it used in teaching music and learning parts, it seems to have also been commonly used by composers themselves. Looking at the score of a Praetorious 4-part Bourrée today, we tend to line up the notes in each part vertically and say, look there's a V chord, etc. But actually the composer was quite possibly thinking horizontally, thinking of writing a part, then another part, then another....not thinking vertically. So, although a choir singing a piece by Josquin de Prez today would all be working with music books, sheets, it's quite possible that many of the choirs singing it in the 16th c. would actually be learning their parts with only one book, or the director would have all the parts memorized and would be teaching them , well; by hand.
Printing became yet cheaper and music books more common in the 17th c. ( At some point a very elegant system of music paper printing was developed that used stretched inked silk threads to create the staff lines). Solmisation of various kinds certainly continued for teaching and learning music: the shaped-note hymns now often known generally as Sacred Harp in the US used a system of four syllables and you can still find Sacred Harp sings all over. But Sacred Harp harmonies were ( and are) typically rather simple. As composed music became more and more complex, with more flats, sharps, and accidentals, solmisation became less useful as a conservatory tool. But early music ensembles have discovered that performance of memorized music has some attractive qualities compared to the sight-read, and are no longer always to be found with their noses pointed into their books.
An excellent book on the 16th c. use of the Guidonian Hand in performance and composing vs. printed music is Anne Smith's The Performance of 16th-Century Music: Learning From the Theorists. New York: Oxford University Press, 2011
An old but useful summary of sol-fa systems and the attempts to modify them to make them useful for increasingly complex music, is over at Google Books: W.G. McNaught's The History and Uses of the Sol-Fa Symbols
There are a few YouTube clips on the Guidonian Hand. Here's a pretty good one showing how it could be used by a choir instead of reading written music. The piece they're doing is one of the mass settings of the popular medieval song L'Homme Armé; I think Dufay's.