Copyright is the legal right that an author or creator of any material has to their creation. You cannot reproduce it without permission... and usually paying them something. In any case, morally and legally, you must always give credit when you use someone else's material.
There are a couple of exceptions to having to get permission to use material. They both fall under the "fair use" rule. If you only quote a small part of their work (usually defined as less than 200 words) you can get away with just giving them credit ("citing" them). The other exception is that faculty can copy materials to be used in class, and individuals can copy materials for their own personal use only.
Hence, it is legal for you to quote others. And it is legal to copy materials if you are going to use them for personal use only.
In the context of research, and writing a paper, you must be very very careful to differentiate between quotes and paraphrases. And you should constantly note down where you got material--that means a full citation, plus page numbers. This is why we are spending some time on MLA and APA.
Failure to cite materials can get you a flunking grade in college. It can get you in jail in the real world. Be very careful to give credit. This even extends to paraphrasing. If the idea is someone else's, give them credit.