How to begin reading Deleuze

I would start with Deleuze's book, Spinoza: Practical Philosophy, because it expresses Deleuze's ethos, his affirmation, his love. You should know what a philosopher loves (Plato would tell you that), and this little book is a love letter from one philosopher to another. Reading it will I hope inspire you to want to read Deleuze, to see how he lives up to "the secret link between Lucretius, Hume, Spinoza, and Nietzsche: their critique of negativity, their cultivation of joy, the hatred of interiority, the externality of forces and relations, the denunciation of power" (Negotiations, 6). 

This frugal, propertyless life, undermined by illness, this thin, frail body, this brown, oval face with its sparkling black eyes­: how does one explain the impression they give of being suffused with Life itself, of having a power identical to Life? In his whole way of living and of thinking, Spinoza projects an image of the positive, affirmative life, which stands in opposition to the sem­blances that men are content with. Not only are they content with the latter, they feel a hatred of life, they are ashamed of it; a humanity bent on self-destruction, multiplying the cults of death, bringing about the union of the tyrant and the slave, the priest, the judge, and the soldier, always busy running life into the ground, mutilating it, killing it outright or by degrees, over­laying it or suffocating it with laws, properties, duties, em­pires -- this is what Spinoza diagnoses in the world, this betrayal of the universe and of mankind. (Spinoza: Practical Philosophy, 12)

After Spinoza: Practical Philosophy, here's what I recommend you read next: 

1. The SEP article on Deleuze (self-promotion warning!)

2. Dan Smith's Introduction to Essays Critical and Clinical; it's also available as Ch 12 of Smith's wonderful new book, Essays on Deleuze.

3. Michael Hardt's Gilles Deleuze: An Apprenticeship in Philosophy, covering Deleuze's early work on Bergson, Spinoza, and Nietzsche.

4. Deleuze's Kant's Critical Philosophy.

5. Jeff Bell's Deleuze's Hume, a nice review of which is partially available here.

6. This might be enough, but if you want two more intro books, there's Todd May and Claire Colebrook.

After that, it all depends on what you're after. 

If you want a rip-roaring, no-holds-barred, thrill-a-minute exercise in polemic and invention, the Marx-Freud synthesis blown to pieces by Nietzsche, then it's Deleuze and Guattari's Anti-Oedipus. (Gene Holland's book on AO is a good companion, but don't forget Deleuze's lecture courses, which are drafts and explications of the concepts. And since I've already self-promoted, I might as well continue: here are my course materials on Deleuze and DG, with outlines and lectures, but no eight-by-ten color glossy photographs with circles and arrows.) 

If you want a guided tour of the universe, covering the cosmic, geologic, evolutionary, developmental, ethological, anthropological, mythological, historical, economic, political, literary, musical, and even more registers, then try A Thousand Plateaus. (Again, Deleuze's lecture courses are a great companion, and aw hell I'm in so deep now it's no use even pretending, you could try Bonta and Protevi, Deleuze and Geophilosophy too. And by this time, Ron Bogue's Deleuze on Music, Painting, and the Arts would be useful. And Elizabeth Grosz, Chaos, Territory, Art.)

But if what you want is the Ur-text, the first book Deleuze wrote in his own voice, after his series of books on other philosophers, then it's Difference and Repetition, where he first brings science and philosophy together. (There are already too many secondary books on DR to be comprehensive here, but let me just mention Hughes, Bryant, Williams, Beistegui, Duffy, Somers-Hall, and Smith again; if there are others to recommend, please add them in the comments. And finally, if you read French, then Sauvagnargues, Zourabichvili, Antonioli, Mengue, Bergen, and I better stop now or this will never end.)