To be honest. When I was like 10 years old my uncle bought me one of the 100 project kits for Christmas. Something like this. ebay.com link: Electronic Project Beginners Starter Kit quality components pack with breadboard

Then in high school I took an electrical and electronics class. There I learned how to read a schematic. Then I've tought myself how to diagnose and repair problems.

I have no knowledge of design. I just follow what's in the books and test things I know.

Edit
Now that I'm in my 30's I've thought about getting one of the design kits for kids, I'm sure that I'd gain so much more knowledge now then when I was 10

I spent 5 years getting my EE degree, but I learned more getting hands on with small electronic projects. Like converting nes to US systems.

Forget engineering. Get a Basic Electronics first year textbook. One for a two-year tech school class.

I started working through this online text, but got distracted - someday I'll get back to it.

http://www.allaboutcircuits.com/

'Make: Electronics' is a good book for beginners - very hands on:

http://www.amazon.com/Make-Electronics-Discovery-Charles-Platt/dp/0596153740/ref=sr_1_1

If you want to learn in order to get a job designing things for commercial use/sale, you will need to attend an accredited university and earn a degree. Most government positions as well as those dealing with safety-related transportation equipment will require PE certification or at least EIT certification.

I second this. I took a couple courses in high school and college, but forgot nearly all of it. Once I got into pinball, I needed to make sense of the schematics and understand why things are wired the way they are (e.g., why are there capacitors across some of the switches?). I picked up that book and the associated kits...
http://www.radioshack.com/make-it-component-kit-1/2760349.html
http://www.radioshack.com/make-it-component-kit-2/2760352.html

It's worth the money for the kits in my opinion. They're pricey, but they're very convenient. Maybe you should wait to buy the second kit until you get to the chapters that need it (second half of the book), but definitely get the first kit when you get the book.

Be forewarned though, the transistors that I got with mine were incorrect, so the transistor-related projects wouldn't work as shown in the book with the parts that they shipped. I ordered my kits about a year ago, so maybe they've since fixed the problem. It's written up in the book's errata...
http://www.oreilly.com/catalog/errata.csp?isbn=9780596153748 (search for "P2N2222A")

After a few exercises in the book, I had the confidence to put down the book and take on my own little project. Now my desk looks like this...
IMG_1054.JPG

Shameless plug: I'm documenting, in excruciating detail, my progress on that project in videos that I'll be posting here...
https://pinside.com/pinball/forum/topic/video-series-designing-and-building-a-new-mod

Engineering is as much art as it is science. While it is relatively easy to learn the science of engineering, it is much harder to learn the art of it.

the picture of that desk certainly has some art to it , as well as science.

I started learning by taking apart VCRs and the like (reassembly optional) and fixing lamps when I was younger. The best way I've found to pick up hobbyist electronics tinkering and troubleshooting skills is to find a project that's interesting enough to you that you'll follow it through to completion and is at the edge of what you feel comfortable with. Start with something simple and either practical or decorative like a motion-activated light switch or an LED cube.

Some more information on what you're trying to get started on would be good, for instance do you have a project machine that needs repairs? Just trying to save on repair costs? Are you considering repairing pins as a hobby or occupation? Just curious? Also be aware that "Electrical Engineering" is a pretty lofty goal for a thing to pick up on the side and there's a reason that both a four-year degree and a further four years of practical work experience is required to even attempt the exam to become a licensed Professional Engineer. Pinball diagnostics and repair is more along the lines of technician work.

If there's one in your area, places like TechShop and other maker spaces usually have classes. Fees, format, equipment available, and skill levels are kind of all over the map, but an intro class would probably get you some good hands-on time if you're starting from an "I know these things exist" standpoint. It'll also probably save you some money up front if you don't already have tools or know what tools you might need. They should also give you some basic safety instruction, which you absolutely should have. If they don't start with that or offer a free safety intro session, call them out on it and ask for a refund.

Soldering itself isn't too hard. Watch a video or two on the web, I'm sure they're available. Practice on bits of twisted stranded wire and then grab a through-hole breadboard (they're also called protoboards) that you can practice soldering and desoldering through-hole connections on. Sparkfun is great for stuff like that. They can be finicky and are worth practicing. The first lab in an an instrumentation course I used to teach was creating a cube out of eight wires twisted and soldered together, saved a lot of time and burnt components (and body parts) in the long run.

Whatever you do, ask questions! It's one of the best ways to learn. Also messing things up and then figuring out how and why it got messed up and what you could do better next time. Also be safe.

I totally agree. A book can teach you the science, but the art has to come from you. I'm a software engineer. I've been trained in that science and I've also been coding since I was 9, so I've had nearly 30 years to learn the art. I've got a sense when something isn't right or isn't complete. Some people call it "code smell"; it's like you're picking up on a scent, something you can't see, but that you know is there.

Not with electronics though. I'm going "by the book". I don't have the nack.

Electronics smells are totally different than code smells, by the way. Magic smoke, and all. More acidic, I think.

Having worked in home restoration and renovation, I can tell you with absolute certainty that learning how to diagnose and repair pinball machines is a completely different animal than "bigger projects around the house." I spent two years of college in computer engineering school before switching to business school, and reading schematics is still very foreign to me. In fact, last night, after three months of pinball ownership, I had my first AHA moment where reading a schematic made perfect sense to me. I credit the above-referenced www.allaboutcircuits.com for that moment. It's rather math intensive, and sometimes feels like homework, but the understanding you will gain, even just in qualitative analysis will be invaluable. It will take some time, but I'm working through it at the same time, so if you have any questions feel free to pm.

Calculating impedence in capacitive+resistive circuits sucks.

*Edit* Actually, I take that back. By far the worst thing I've had issues with as a non-math person has been calculating the phase angle of A/C circuits with capacitors and inductors in play. I really feel sorry for people that work on alternating current crap.

That's why sound is often the hardest thing to fix in a pin.

Electrical Engineering and my BSEE took 5 years at college. Unfortunately it wasn't electronics but rather power engineering (transmission lines, substations, switchgear, etc.). Still learning even though it's been 27 years since I graduated.

I completely agree. 5 years to get a degree in Electrical and Computer Engineering. I work in marketing now but I still know who Kirchoff was!

The vast majority of practical electronics knowledge I picked up as a kid reading the Radio Shack quick guides (basically the same thing as the new Make guides they sell). Those will give you everything you need (and more) to sound smarter than most EEs out there. A simple project kit will give you enough comfort-level to repair most consumer electronics including pins. Just do everyone a favor and shop at your local Radio Shack. We're in real danger of losing these guys for good.

Also:

Bally F.O. ### Repair manual

Williams Repairing Electronic Pinball Machines

and the Gottlieb game repair manual

Fluke meters are great.
Weller makes god soldering equipment.