This book is deceptively simple, and didn't necessarily teach me any one thing I didn't already know, BUT it emphasized HOW, WHEN, and WHY to use each technique, and my writing has immensely improved as a result.
I've recently read through the book "They Say/I Say", and it's a book that was literally written to answer this exact question. If you don't have time for the book, there's a great summary of the templates it presents (and the reasoning behind them) at this link here.
Pretty much guarantee if you use that list as a checklist and ensure you're covering those points you'll end up with a strong section.
It will vary by course and prof, but so far mine have been:
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Annnnnd that's as far as I've gotten! Best of luck; knowledge is priceless :)
Goodreads bot is not linking the right book. Here it is: https://www.amazon.com/They-Say-Matter-Academic-Writing/dp/1469028611
Yeah, that's a tricky one. My impression is that many schools and colleges have adopted <em>They Say, I Say</em>, which encourages the use of first person. But many teachers are under the impression that first-person pronouns are bad, though I imagine most of them would be hard-pressed to explain why they are so bad. I can see why the convention exists in science writing and a few other contexts, but it seems silly to proscribe first-person pronouns in an essay that's asking for a student's opinion. I have found in my own classroom (I teach research to high school freshmen) that certain parts of the paper become much clearer and more natural when the students write in first person.
Anyway. As for avoiding it: most of the time you can just cut the "I believe" or "I think" or "I feel that", and keep whatever comes after it. E.g.
I also recommend checking out the book I mentioned above. It contains tons of templates that are quite useful to students, and not all of them involve first-person pronouns. If you Google "they say I say templates" you'll find PDFs of those templates. I have also used some of the sentence stems from this website.