If you're sure of your topic, then you can go straight to the online catalog to look for books or to the periodical indexes and electronic resources to look for articles. If you're not sure, then you may want to look at some encyclopedias or browse through some magazines. Either way, you should have a clear idea of what you want to accomplish before you go through the library doors. Second, make sure you've given yourself enough time to accomplish your mission. It's unrealistic to think that you can stop into the library and find several articles on a topic in fifteen minutes.
Good research takes time.
It's hard to do research in bits and pieces, so don't try to do it piecemeal if you can help it. You might be pleasantly surprised to find out that it took less time than you expected, but you don't want to do things in a rush and make mistakes. You'll find that searching for information takes less and less time as you become more and more adept at research. Next, make sure you have everything you need. All simple things, but easy to overlook.