I am a self-taught photographer, which isn't to say that other people haven't helped me or taught me things but I haven't taken any formal classes, just a lot of reading, poking around on the web and asking questions.
The most important aspect of teaching yourself photography is taking what you read and going out and playing around with it until it clicks for you, and then coming back and looking critically at the results to learn what to do differently the next time.
My favorite resource is the photo board I am part of, it is a wonderful group of women, but to keep things safe for all of us we have decided to make the board private. I would recommend finding a photography board out there on the web (and I am sure there are millions) that you feel comfortable in.
ILP is a great one if you are into child portrait photography
Martin Bailey has what looks like a great one, I haven't had time to do more than poke around on there though, but don't leave without checking out his podcasts, they are full of GREAT information.
2 Peas - General Photography 2Peas is mainly about scrapbooking but the photography forum is full of talent they also have a great class on there called 12 weeks to better photos, ideal for just starting out photgraphers
The Pioneer Woman while not a message board is full of photography information and tips
Flickr is one of my favorite photography websites these days, tons of groups to join about all kinds of cameras, photography styles and subjects, and mountains of inspiration. Check out the explore page to be blown away by the talent.
So what was my actual process? I started out by doing some basic reading of what aperture, shutter speed and ISO are and how they impact your photo both in terms of exposure and the look of the image. You can read about that on PW, the lessons on 2Peas, in Understanding Exposure by Bryan Peterson, I personally read about it here. That stuff clicked for me pretty quick being an engineer so I just went out armed with my camera and manual (to help me learn how to change my settings) and started shooting.
I made a commitment to myself that I was going to learn photography so since I was pretty sure what the aperture did, and what shutter speed did, I started playing in the aperture priority (Av on Canon) and shutter priority (Tv) modes, I didn't use the auto modes at all. In Av or Tv you pick the aperture or the shutter speed and the camera picks the other one for you. I shot in these modes for a long time, about 9 months. During that time I also learned to play with my ISO. Eventually being the control freak that I am I decided it was time to venture into manual mode, and that is how I shoot now, I rarely use any other mode. Manual seems daunting at first, but really it isn't, at least I always know what settings I am using now, not letting the camera choose things for me that might change how my image looks. I will write a post soon about venturing into manual, I think it is a big enough step that it deserves it's own post.
Now I had a lot of images, and some idea how my camera worked the next step was to keep improving them. Look at them critically to see what worked and what didn't and what settings you should use the next time. Find what you like about them that you want to remember to repeat in the future. This is when I good message board comes in handy, you can post for constructive criticism and also give it to others which will help you learn to give it to yourself.
I will be back soon with more info, maybe I will tell you about the thing that I learned that has totally changed my shooting and really made my results shooting in manual much more consistent, and about going manual.