As I suggested for your other question, a study group would be a good option. (Or maybe your professor would be more approachable during office hours rather than during the lecture?)
Your textbook probably has examples that will be most immediately helpful for you. You can look up examples online (Wikipedia probably has some, as well as various other resources). The term you're looking for is "constituency" and "constituency tests". That's all you need to know. But it really does vary for different classes/textbooks so you might do it "wrong" by doing it a different way. I know that can happen because I've seen my students do it when I've taught them this.
Basically movement and substitution tests (see examples elsewhere) are designed to minimally change the sentence but show flexibility of one component (constituent). Another option is coordination, saying "I like pizza" > "I like pizza and pasta". If you can coordinate it, it is usually a constituent. (That test is easy, but once in a while it gives false-positives, for non-constituents that happen to allow coordination like "John likes pizza, and Mary pasta." So be careful with it.)
Personally my favorite constituency test, though not one you should be using as a main reason on your homework or on an exam, but one that might make it a little more intuitive, is the "book title test"-- could a book possibly be called that? If so, it's a constituent. (Someone told me that someone had looked at the titles in the Library of Congress and found something like only 3 titles that aren't constituents, odd names like "I Have The".) So start with that to get an idea about it, then see if you can show the same results with the other tests (and verify you were correct).
Constituency tests are not particular difficult, but they do take some trial and error to understand, so start with that. Keep applying them until it starts to make sense, comparing examples in your textbook to your results.
