How would you self teach yourself electrical engineering?

Learning Electrical Engineering by yourself is much better than going to school, because you can choose the books and style of learning that you want. The most difficult part is finding out what works for you. I taught myself electrical engineering and now work in a firm as an electrical designer, and I am now on my way to getting my PE License. For me the most difficult part was teaching myself the mathematics and physics. It took me a long time to find the right way to learn these subjects on my own, but once I figured it out, I flew through the learning process, and was able to get my first job. I used these 2 books: Engineering Mathematics, and Advanced Engineering Mathematics by K.A. Stroud. These books teach you all the mathematics and physics that you could ever need, and they use a programmed approach to teaching that make it somehow painless to learn even the most complex subjects.

Now you have to learn how to apply your new found mathematical skills, which really you can do anything with, but since you want to go into Electrical Engineering I advise that you get the most basic easy to understand book about electricity ever written, Basic Electricity by Van Valkenburgh. After you have a good grasp of this book you should be ready to decide what specific area of electrical engineering you want to go into. Electrical Engineering is a very large field, but as long as you have a grasp on the mathematics and physics involved you should be able to go into any area you want. There are two major categories to choose from, Electronics or Electrical Engineering. Electronics is concerned with small circuits often found in modern technology. Electrical engineering is concerned with much bigger things like power supply, and distribution, and electrical infrastructure.

The next thing you need to do is start applying for internships or any kind of job at an engineering firm. If you can prove that you know the mathematics and have a grasp on electricity, you should be able to get your foot in the door some how. Once you are in you have to work under a licensed PE for 3 years, and then you will be eligible to take the Fundamentals of Engineering exam, which you should be able to pass as long as you have kept learning for those 3 years. Then a few years later, forgot exactly how many more, you will be eligible for the PE exam. Once you pass this exam you will be a Licensed professional engineer.

Seems like a long road, but even if you go to school, you still have to take the FE exam, and the PE exam. Becoming an engineer in general takes a long time, and takes a lot of passion. I got there this way, and would recommend it over school, because you start getting professional experience sooner, and you avoid a lot of useless classes and fees.

A good way to gauge your progress is to look up the FE exam requirements and see what you need to know.