LondonKings

This, of course, is the fundamental hacking skill. If you don't know any computer languages, I recommend starting with Python. It is cleanly designed, well documented, and relatively kind to beginners. Despite being a good first language, it is not just a toy; it is very powerful and flexible and well suited for large projects. I have written a more detailed evaluation ofPython. Good tutorials are available at the Pythonweb site; there's an excellent third-party one at Computer ScienceCircles.
I used to recommend Java as a good language to learn early, but thiscritique has changed my mind (search for “The Pitfalls of Java as a First Programming Language” within it). A hacker cannot, as they devastatingly put it “approach problem-solving like a plumber in a hardware store”; you have to know what the components actually do. Now I think it is probably best to learn C and Lisp first, then Java.
There is perhaps a more general point here. If a language does too much for you, it may be simultaneously a good tool for production and a bad one for learning. It's not only languages that have this problem; web application frameworks like RubyOnRails, CakePHP, Django may make it too easy to reach a superficial sort of understanding that will leave you without resources when you have to tackle a hard problem, or even just debug the solution to an easy one.
If you get into serious programming, you will have to learn C, the core language of Unix. C++ is very closely related to C; if you know one, learning the other will not be difficult. Neither language is a good one to try learning as your first, however. And, actually, the more you can avoid programming in C the more productive you will be.
C is very efficient, and very sparing of your machine's resources. Unfortunately, C gets that efficiency by requiring you to do a lot of low-level management of resources (like memory) by hand. All that low-level code is complex and bug-prone, and will soak up huge amounts of your time on debugging. With today's machines as powerful as they are, this is usually a bad tradeoff — it's smarter to use a language that uses the machine's time less efficiently, but your time much more efficiently. Thus, Python.
Other languages of particular importance to hackers include Perl and LISP. Perl is worth learning for practical reasons; it's very widely used for active web pages and system administration, so that even if you never write Perl you should learn to read it. Many people use Perl in the way I suggest you should use Python, to avoid C programming on jobs that don't require C's machine efficiency. You will need to be able to understand their code.
LISP is worth learning for a different reason — the profound enlightenment experience you will have when you finally get it. That experience will make you a better programmer for the rest of your days, even if you never actually use LISP itself a lot. (You can get some beginning experience with LISP fairly easily by writing and modifying editing modes for the Emacs text editor, or Script-Fu plugins for the GIMP.)
It's best, actually, to learn all five of Python, C/C++, Java, Perl, and LISP. Besides being the most important hacking languages, they represent very different approaches to programming, and each will educate you in valuable ways.
But be aware that you won't reach the skill level of a hacker or even merely a programmer simply by accumulating languages — you need to learn how to think about programming problems in a general way, independent of any one language. To be a real hacker, you need to get to the point where you can learn a new language in days by relating what's in the manual to what you already know. This means you should learn several very different languages.
I can't give complete instructions on how to learn to program here — it's a complex skill. But I can tell you that books and courses won't do it — many, maybe most of the best hackers are self-taught. You can learn language features — bits of knowledge — from books, but the mind-set that makes that knowledge into living skill can be learned only by practice and apprenticeship. What will do it is (a) reading code and (b) writing code.
Peter Norvig, who is one of Google's top hackers and the co-author of the most widely used textbook on AI, has written an excellent essay called Teach Yourself Programming inTen Years. His "recipe for programming success" is worth careful attention.
Learning to program is like learning to write good natural language. The best way to do it is to read some stuff written by masters of the form, write some things yourself, read a lot more, write a little more, read a lot more, write some more ... and repeat until your writing begins to develop the kind of strength and economy you see in your models.
I have had more to say about this learning process in How To Learn Hacking. It's a simple set of instructions, but not an easy one.
Finding good code to read used to be hard, because there were few large programs available in source for fledgeling hackers to read and tinker with. This has changed dramatically; open-source software, programming tools, and operating systems (all built by hackers) are now widely available. Which brings me neatly to our next topic...

I'll assume you have a personal computer or can get access to one. (Take a moment to appreciate how much that means. The hacker culture originally evolved back when computers were so expensive that individuals could not own them.) The single most important step any newbie can take toward acquiring hacker skills is to get a copy of Linux or one of the BSD-Unixes, install it on a personal machine, and run it.
Yes, there are other operating systems in the world besides Unix. But they're distributed in binary — you can't read the code, and you can't modify it. Trying to learn to hack on a Microsoft Windows machine or under any other closed-source system is like trying to learn to dance while wearing a body cast.
Under Mac OS X it's possible, but only part of the system is open source — you're likely to hit a lot of walls, and you have to be careful not to develop the bad habit of depending on Apple's proprietary code. If you concentrate on the Unix under the hood you can learn some useful things.
Unix is the operating system of the Internet. While you can learn to use the Internet without knowing Unix, you can't be an Internet hacker without understanding Unix. For this reason, the hacker culture today is pretty strongly Unix-centered. (This wasn't always true, and some old-time hackers still aren't happy about it, but the symbiosis between Unix and the Internet has become strong enough that even Microsoft's muscle doesn't seem able to seriously dent it.)
So, bring up a Unix — I like Linux myself but there are other ways (and yes, you can run both Linux and Microsoft Windows on the same machine). Learn it. Run it. Tinker with it. Talk to the Internet with it. Read the code. Modify the code. You'll get better programming tools (including C, LISP, Python, and Perl) than any Microsoft operating system can dream of hosting, you'll have fun, and you'll soak up more knowledge than you realize you're learning until you look back on it as a master hacker.
For more about learning Unix, see The Loginataka. You might also want to have a look at TheArt Of Unix Programming.
To get your hands on a Linux, see the Linux Online! site; you can download from there or (better idea) find a local Linux user group to help you with installation.
During the first ten years of this HOWTO's life, I reported that from a new user's point of view, all Linux distributions are almost equivalent. But in 2006-2007, an actual best choice emerged: Ubuntu. While other distros have their own areas of strength, Ubuntu is far and away the most accessible to Linux newbies. Beware, though, of the hideous and nigh-unusable "Unity" desktop interface that Ubuntu introduced as a default a few years later; the Xubuntu or Kubuntu variants are better.
You can find BSD Unix help and resources at www.bsd.org.
A good way to dip your toes in the water is to boot up what Linux fans call a live CD, a distribution that runs entirely off a CD without having to modify your hard disk. This will be slow, because CDs are slow, but it's a way to get a look at the possibilities without having to do anything drastic.
I have written a primer on the basics of Unix and the Internet.
I used to recommend against installing either Linux or BSD as a solo project if you're a newbie. Nowadays the installers have gotten good enough that doing it entirely on your own is possible, even for a newbie. Nevertheless, I still recommend making contact with your local Linux user's group and asking for help. It can't hurt, and may smooth the process.