I kind of have an idea of when 了 and 过 should be used but it's mostly on a case by case basis, and I don't know the exact rules.
So if I want to express something that happened in the past, when should I use 了 and when should I use 过?
There are multiple uses for both 了 and 过, so it's good you are just asking about usage to express past action or events. 了, as you probably know, is often used to express a change of state. Perhaps somewhat relatedly, 了 can be used to express a past action that is still ongoing. But 过 cannot: when 过 is used to refer to a past event, that past event must have completed. Additionally -- and most distinctly -- 过 is used to express having had the experience of something, rather than a particular instance. As a simple example, consider the difference between
Here the same structure is used intentionally.
When combining them, it emphasizes the completion of a single action or event. So, for example,