Rules for verb usage

I'm fairly new to the world of linguistics and this is my first post in this forum. I've been helping a friend to learn English and one of her questions has me stumped, even as a native speaker. She is confused about which verb forms to use. She understands all of the tenses and can create simple sentences in each tense, however she struggles with complex sentences and sentences where multiple verb forms are used. Is there a name for this field so I can do some further reading? Can anyone suggest any materials that explain the rules?

An example sentence that I found in an article online:

George Lucas had considered bringing Mark Hamill back as Luke Skywalker.

Upon seeing this sentence, my friend would probably ask why we use "bringing" instead of "brought" or "considered to bring"?

I'm sure there must be rules about which verbs should be used after one another. Any help would be greatly appreciated.

Thanks,