For someone new to anarchism, the sheer breadth of thinking makes it very hard to understand its basic tenets. This really excellent anthology by Daniel Guerin, who, incidentally, wrote one one of the best short guides to anarchist history and theory, "Anarchism: from theory to practice", is a wonderful guide to the range of ideas.
Some of the book is arranged so as to present the ideas of particular thinkers, including (as MightyBoosh says), Proudhon, Bakunin (touching on his famous controversy with Marx within the First International), Kropotkin and Malatesta. Other parts of the book are arranged thematically to consider issues such as the Spanish collectives, the Kronstadt uprising, and anarcho-syndicalism.
The collection of documents from a wide range of sources and ages gives the book a sense of immediacy as well as outlining the history and development of anarchist thought. Of course, some aspects will appeal to you more than others, but I've found the book really useful in understanding what united and separated different writers, and in helping me follow up strands of thinking or activism that I might never otherwise have heard about.
I'd warmly recommend the book to anyone who wants to find out about anarchism, or who knows a little but wants to expand their understanding.