How do I avoid plagiarism and use quotations and paraphrases correctly?

First, for an educator to provide answers using the exact quotation you are assigned as part of your homework would be an example of precisely the sort of academic dishonestly your instructor is teaching your how to avoid. Thus for this answer I will use the following quotation: 

It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife.

This is the first line of Jane Austen's novel, Pride and Prejudice. 

If you want to refer to this line in an essay you can quote all or part of it or paraphrase it. Simply using the line without properly attributing it to Austen would be an example of plagiarism. 

You could paraphrase this passage by saying: "According to Jane Austen, every one agrees that wealthy bachelors should marry." Although the paraphrase has only one word ("that") in common with the original, it expresses Austen's key points. 

You also have the option of quoting the entire passage as a block quotation or using ellipses to incorporate a partial excerpt into one of your own sentences, e.g. "... a single man ... must be in want of a wife". 

Whether you quote or paraphrase Austen, you need to cite the work from which your quotation is taken according to a specific style sheet. Among the most common used in North American universities are MLA, APA, and Chicago.