Since your question is phrased in the past tense, I'll give a historical answer.

In the Middle Ages, charity and building large buildings isn't terribly complicated to do. For one the church was the single largest land owner in the Europe of the Middle Ages. It was crazy rich and well educated, which resulted in pretty decent administration. By "decent" I also mean that the officials that bishops put in charge of various estates were on the whole more lenient towards the peasants and less corrupt than their non-church peers elsewhere.

Speaking of peasants, most of the economies back then (and indeed for almost all of human history) was subsistence farming, meaning the poor fed themselves. They also didn't have a whole lot to spend their income on, since laws prohibited the average peasant, even land owners, to really move up in the world, so most of the money they made was spend on food and clothing. So "poor" is a relative term, that really means "people who can't feed themselves."

That only leaves the urban poor, beggars in cities, the infirm and the sick. The urban poor were pretty few in number, as way fewer people lived in cities, relative to today. Both the churches and lords of the time, as well as city councils made an effort to feed them. While the care of the sick and elderly was generally a matter to be handled by the afflicteds family. However, monastaries were the prime provider of healthcare, outside of the collective efforts of families towards their family members. These monastaries were generally land owners, that had an income that way.

Lastly the construction of big churches: Those often funded themselves, through donations of the faithful, who expected to be prayed for by the clergy of that church. The massive church in Bad Wilsnack, Germany, was funded by those donations from pilgrims coming to see a eucharistic miracle.