That said, software engineering is one of the fields you can get employment without a degree, provided you can 'show your work'. The hard part is building up your skills in a way that can easily be demonstrated. The common wisdom these days is to create a github profile, build some interesting things, commit to some open-source libraries, and use your profile as a resume of sorts.
Here's interesting article on being a well-rounded programmer:
We're also in a 'golden age' of self-guided learning, with online tools to help learning galore, here are a few:
Also, get a few decent books on "Programming 101". Common wisdom suggests you learn C, one of Ruby/Python, Java, and a functional language like Haskell. Here are some good books to learn from:
The C Programming Language (some people say you should start here, I'm one of them!):
I hope you do choose programming as a career, its been very rewarding for me :)
Rinse repeat. You'll find that once you have one language down, the process will go much faster with the second. The features and syntax of most languages are pretty similar.
You can pick any language you like to start with, but personally I'd recommend starting with a hard typed compiled language rather than a dynamic language. Dynamic languages are easy to learn, but its easy to be a lazy and bad programmer in them. They let you get away with too much. Hard typed compiled languages are a) much better at catching your errors and b) much harder to be a lazy programmer in. They don't let you get away with things nearly as much.
I'd recommend Java, seems to be the language a lot of people start with. It will also give you a good founding in open source programming. I started with C/C++ and I'm glad I did. But that was more of a challenge - had to learn pointers and memory management in my first language. And after that I took a little while to learn the open source mindset, since I'd started in a procedural language.
Once you have a good grasp of an object oriented language like Java (or Python) and what object oriented programming means, then I'd recommend reading the Gang of Four book on Design Patterns (http://www.amazon.com/Design-Patterns-Elements-Reusable-Obje...) and Martin Fowler's book on Refactoring (http://www.amazon.com/Refactoring-Improving-Design-Existing-...). Those will give you a pretty good basis in software design and maintenance.
In terms of recommended reading for learning a language, the O'Reilly books are nearly always good in my experience. Here's one for Java (Learning Java: http://www.amazon.com/Learning-Java-Patrick-Niemeyer/dp/0596...) and here's one for Python (Learning Python: http://www.amazon.com/Learning-Python-Powerful-Object-Orient...)
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