Before the Catholic Church set up the system of parishes so that every geographical area had a church with a pastor, some benefactors would set up their own places where priests could live and minister to the surrounding population. Another benefit/motivation was for the priests to pray for the souls of the founder and his family.
This was not the same as a monastery, although they were often referred to in England as "minsters" which derives from the Latin monasterium. The canons were what we would now call parish priests, not monks with a vow of poverty. In fact, each resident canon would receive a salary for their needs.
The financial support for the collegiate church was often an endowment by a wealthy patron, but could also be donations. Charny's no doubt intended to rely on donations from pilgrims who came to see the cloth that wrapped the body of Christ, and the purchase of souvenirs like the pilgrim badge shown yesterday. A collegiate church could also provide a hospital or school which would generate revenue.
Collegiate churches needed a set of rules to maintain order and explain the roles of different members, and they found a template in the works of Bishop Chrodegang of Metz. Chrodegang was chancellor to Charles Martel and instrumental in a spiritual revival in the Kingdom of the Franks. In 755 he wrote a Regula Canonicorum, "Rule for Canons," based on the Rule of St. Benedict, not for a monastic community but for secular clergy. Chrodegang's rule was popular for a time, even appearing in Ireland (a rule attributed to Máel Ruain looks like it was based on Chrodegang's). By the time that Charny was founding his church, Chrodegang's rule was being abandoned in favor of rules first promoted by Augustine of Hippo.
Individual positions in a collegiate church could also be supported by a prebend, a gift of income from a specific source, such as a piece of property. For a more detailed explanation of prebends, come back tomorrow.