The two most important QFT's are Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD).
Other than enrolling in an accredited Graduate Program in Physics, there are printed resources out there that can help you understand the nuts and bolts of this great intellectual achievement.
First, master the Mathematics of Quantum Mechanics, and Special Relativity.
UPDATE: Then read the middle so-called "Hard parts" of Peter Woit's book: Not Even Wrong. In brilliant expository style, he explains (in prose form alone) how QFT came to be, beginning with the mathematics involved, notably Herman Weyl's Group Representation Theory.
Then, read “Quantum Field Theory Demystified, a Self-Teaching Book”, by David McMahon, available in bookstores and targeted to the very intelligent layperson.
UPDATE: Pursuant to Peeter Joot's first comment to this blarticle, QFT Demystified is held in rather low regard by Professional Mathematical Physicists. Peeter suggests playing a "find the Errors" game with it. Sounds like fun Peeter! I'm up to it! One can get a considerable start by reading the comments to the book at it's Amazon page. To Peeter, I agree with your comments re McMahan's QM Demystified, I never bought it.
As early as page 3 McMahon makes mention of the Klein-Gordon equation with its obvious flaws, and moves quickly into the Dirac Equation, which unified Quantum Mechanics and Special Relativity and gave birth to QFT.
On page 4 he explains that while position “x-carat” is considered an operator and time “t” a parameter in QM, and one would expect the promotion of “t” to operator status in QFT, that instead “x-carat” is considered a parameter as well, and McMahon goes on from there through its slim but lovely 261 pages.
A most popular book is "Quantum Field Theory in a Nutshell," by String Theorist Anthony Zee. I would not attempt this book without first mastering Mahon's work. I also own “Nutshell” as Zee refers to his book, and find it as others do a book than likely began in intent as a non-technical popular overview of QFT, then morphed somewhere along the way into a “near”-textbook without quite achieving true textbook status. Nevertheless Zee's humor is infectious, and I enjoyed it, but it is not as important as the following:
For a more Mathematical and better treatment as a textbook, Peter Woit recommends textbooks by Pierre Ramond, Peskin-Schroeder, and V.P. Nair. D.R. Lunsford recommends Michele Magiore and "Advanced QM" by Schwabi.
A wonderful discussion on QFT texts based on Zee's announcement that "Nutshell" will be re-released in 2010 with a new introduction can be found at Peter Woit's blog "Not Even Wrong" here
UPDATE (Dec. 25, 2009): I typed in "Quantum Field Theory" at Amazon and the following books came up in the following order. I would appreciate a Professional commenting on the better ones (in addition to those already mentioned), with thanks in advance.
They are (as of today):
Quantum Field Theory by Mark Srednicki (Hardcover - Feb 5, 2007)
Quantum Field Theory in a Nutshell by A. Zee (Hardcover - Mar 10, 2003)
Quantum Field Theory Demystified by David McMahon (Paperback - Feb 29, 2008)
An Introduction To Quantum Field Theory (Frontiers in Physics) by Michael E. Peskin and Dan V. Schroeder (Hardcover - Oct 1, 1995)
Quantum Field Theory by Lewis H. Ryder (Paperback - Jun 13, 1996)
The Quantum Theory of Fields, Volume 1: Foundations by Steven Weinberg (Paperback - May 9, 2005)
A Modern Introduction to Quantum Field Theory (Oxford Master Series in Statistical, Computational, and Theoretical Physics) by Michele Maggiore (Paperback - Feb 10, 2005)
Modern Quantum Field Theory: A Concise Introduction by Tom Banks (Hardcover - Oct 27, 2008)
Quantum Field Theory I: Basics in Mathematics and Physics: A Bridge between Mathematicians and Physicists (v. 1) by Eberhard Zeidler (Hardcover - Sep 1, 2009)
Introduction to Classical and Quantum Field Theory (Physics Textbook) by Tai-Kai Ng (Paperback - May 18, 2009)
A First Book of Quantum Field Theory, Second Edition by Amitabha Lahiri and Palash B. Pall (Hardcover - Sep 2, 2005)