You must cite all ideas that are not your own -- not just when you are quoting but also when you are paraphrasing. Otherwise it is plagiarism (see below).
Most often, the problems of citation I run into result not from deliberate plagiarism but from ignorance about or incompetence in citation. In the end, citation is an art like writing style. And, as with style, the best advice is to model oneself on writers (citers?) who do it well. Here is an especially good, if sketchy, resource on citation in general.
With students, the problem is often too little citation. They have too few sources, and they don't know how to deal with citing the same source over and over again. (Solution: (A) use a footnote that says something like "the next few paragraphs draw on Smith (1976)" or, better yet, (B) get more sources.) Among academics, the problem is often at the other extreme: too many citations. In the end, citation is part of the rhetoric of writing. It serves functions beyond just attribution. Good citation can help the reader locate the paper's argument within the literature. By invoking the weight of authority or by providing a mechanism for spin, citation can also help you make your argument. (My favorite example is the minimization strategy. When you are saying something that adds little or nothing to a previous author, cite your source on some narrow point only, thus providing due attribution while making your own contribution look bigger. I have been the victim of this strategy on more than one occasion.) The worst offense, however, is piling on references, as decoration or to show how much you have read. The mark of an amateur. A good referee will see this for what it is, and it will count against you.
Citation style.
You should cite references using the “scientific” or name-date style, which is dominant in economics. Rather than placing a reference in a footnote, you should follow the idea you are citing with the name of the author and the date of publication of the work cited. Example:
Far from being the inventor of the idea of perfect competition, Adam Smith was in fact among the last representative of economists who saw competition as a dynamic process of rivalry (McNulty 1967).
This means you are citing a 1967 article by someone called McNulty as the source of the idea in the sentence. You would then list that article in a list of references at the end of your paper:
McNulty, Paul J. 1967. “A Note on the History of Perfect Competition,” Journal of Political Economy 75(4): 395-399 (August).
There are many ways to run the details of a name-date style. Pick one style and use it consistently. Here is the famous Turabian guide.
Some of your references will no doubt be available online, and there are standards for citing online resources as well.
Plagiarism.
The UConn student conduct code defines plagiarism as “intentionally or knowingly failing to properly credit information, research or ideas to their rightful originators or representing such information, research or ideas as your own.” Here are some resources from the UConn Libraries.