When you see the instruction to "use MLA style," for instance, that means your paper itself as well as your citations need to look a certain way. (There are even rules documenting when to write out numbers or preferred phrasing and things like that, but we won't get into that here.)
If you don't see a style guide named in your assignment, ask your professor what they'd prefer! MLA is the most frequently used in our classes, but it depends on the subject! Psychology and speech classes frequently prefer APA, while history and art history may have you use Chicago Style.
When do you need to insert an in-text citation? Every time you use information not original to you. "Quotes" are a major red flag pointing out where citations need to appear, but even if you paraphrase, you need to give credit! It's about ideas, not just language. When you quote, you're borrowing ideas and words; paraphrase, you're borrowing just the ideas... but you are still borrowing something from another creator.