Can someone please explain how harmony works in Renaissance music?

Thanks.

Not really different from the classical period. Harmony arose from counterpoint and polyphony and you will find stretches of homophonic writing in Palestrina and others. Octaves and fifths were frowned on as they were later which doesn't mean that the masters always obeyed the rules.

Certain rules seem to have been followed like always ending on a tierce de picardy with a minor mode which meant sharpening the 3rd of V when it became the leading note -and the 3rd of VI leading up to it.

In the early period two note harmony was far more widely used than triadic harmony. Melodies with drone accompaniments were the order of the day in a lot of folk music and melodies were woven together to produce polyphony which gave the listener a good idea of the form of the work as well as producing some breathtakingly beautiful effects. As keyboard instruments developed and became more widely used the three note harmonies became the norm and chordal music was used to accompany melodies. Some sounds were considered unacceptable still, and cadences were very different from the later ones of the Baroque. It was more usual to end a piece on keynote only rather than with a full chord. The best way to understand the use of harmony in the Renaissance is by listening to as much as you can. If you can get your paws on some scores you can analyse what was written too. Great fun!