For learning proper touch-typing, I would initially suggest you work on accuracy over speed. Really force yourself to use the
proper fingers, especially for the central keys (B, Y and others). That step can be accomplished fairly quickly, within a week or so. Increasing your speed is a much, much longer process. Your goal is to reach a point where typing becomes effortless and accurate; words will pour fourth onto your screen simply by willing it.
It pains me to see how badly most people type, and it is really worth the effort to raise your level competence. I'm actually a fan of taking a classroom typing course, since the skill lends itself well to a structured learning environment. See if any local community colleges offer a night course - a few weeks in that sort of environment will improve your typing dramatically.
My suggestion of playing The Typing of the Dead is serious, but only after you build your proficiency in the technique up. Typing games are a great way to improve your speed, but it is easy to "cheat" and use bad technique, which will ultimately set you back.
Here's a $10 buy it now sale for tTotD. I wouldn't really spend more than that.