Learn a framework for developing web applications. Specifically, learn Django.
This is because most new applications are web applications, and because you can write a satisfying application without knowing much. Also, you get immediate feedback on your code -- you can see whether or not the app is coming out the way you want.
Django is recommended because (a) it is written in Python, (b) it is relatively popular, and (c) it is similar to Rails, which is very, very popular and thus easy to get hired for.
(in parallel with 1) Decide on an application that you want to write, and write it. Put the code on Github or Gitorious or Bitbucket (as you go -- not just once you finish).
If you are exited about getting involved in free and open source software, it's usually best to work on a project that you actually use. That way, you at least understand some of how users expect the program to work. Unfortunately, the programs that you use are likely to be the ones used by zillions of other people, so much of the low-hanging fruit will be already plucked. But maybe you have a more obscure interest which involves software? For instance, I have added features to electronics schematic software, vector graphics software, an interactive fiction virtual machine, a search engine, and a bunch of other random stuff. If you don't see a feature you want to add or a bug you want to fix, just take a look on the bug tracker and see if anything catches your eye. Don't worry if you can't fix any given bug; if it were easy, someone would have done it already!
This is because most new applications are web applications
Or smartphone/tablet apps? Many of which are just web apps reskinned for a phone, but there's a lot that aren't. But I don't know the industry enough to say which is bigger these days, in terms of either developer jobs, or new ideas waiting to be plucked from the tree of knowledge.
Lots of people (particularly people associated with LessWrong) are telling me I should become a computer programmer; in response I've taught myself a little Python using this site, written a couple Python scripts on my own, and just now sent in an application to App Academy. But if I don't end up going to App Academy, what's the best way to develop some actually marketable programming skills? I've heard people recommending getting involved in open source projects on Git Hub, but when I looked at Git Hub I found it overwhelming, with no idea of how to find a suitable project to work on. Advice?