I found out that I liked economics shortly after I graduated from engineering, before which I had a completely skewed and cynical view of economics and economists, informed mainly by writers of left-wing books (who generally aren't economists). Fancying myself as a bit of an auto-didact, I tried to self educate. I bought textbooks, read articles from the net, read blogs, etc.
But if you're anything like me, then you will skip over all the boring fundamentals and read the more advanced, but interesting sections. Economic literature is written in such a way that the literate layman can be fooled into thinking he understands the material. There are specific terms used by economists (eg. economic profit) that has an entirely different definition than the common one (eg. economic profit takes into account opportunity costs). So I'd be reading these articles thinking that I'm getting it, but really I was missing 50-80% of what the guy was trying to get at, because I just had no idea or training in economic thought.
I spent 5 years doing this. There was no watershed moment where I realised this was the wrong way to go about it. Ironically I actually became so interested in economics that I enrolled in a graduate diploma 2 years ago (which is essentially an undergraduate economics degree for people with a degree in something else).
In my first semester, I had to correct a shitload of misconceptions that I'd harbored over the years. It was like doing double the work - challenging the material presented against my ill-informed positions, then fact checking and reasoning out which was correct. I was wrong most of the time, but there are positions that I still hold that university economics hasn't beaten out of me (like infant industry protection - for some reason uni economists are all staunchly pro-free trade, and they really only gloss over the alternatives).
So 2 years on (and 1 year to go), I feel that I'm in a position to offer some advice about learning (mainstream) economics. If you go the self-learning route:
1) Make sure you get a good grounding on the fundamentals of micro and macro. Any uni textbook is probably okay... that free Intro to Economic Analysis book is pretty good (I used it as a second textbook for my intermediate micro class). But the bottom line is read EVERYTHING and don't skip stuff because it's boring. They are often the most important parts...
2) A decent book for a general audience is "Economics in One Lesson" by Hazlitt. If you don't know what opportunity cost is, then you'll never forget after he's drilled it into your head a thousand times.
3) If you're serious about learning econs, I'd steer clear of popular books like Freakonomics and the Logic of Life. They're fun and enjoyable to read, but not particularly rigorous and occasionally quite dodgy.