Hi, Andy. Some components of a circuit board are resistors, capacitors, diodes, LED's, IC's, inductors, relays, and transistors and most look totally different when comparing these items to a through hole board and a surface mount board.
Not only do you have to learn about the components themselves, but direct current (DC) and alternating current (AC), and how an individual component, a circuit, or a circuit block works and interacts with other circuits or blocks. Some components react differently between the different types of currents too.
I stuffed "learn electronics" into Google, and that came up with a list of online sources for learning. Peruse that and find the best result that works for you.
One thing I highly recommend is getting your amateur (ham) radio license. The material is presented in a way that anyone can learn it, and includes electronics, radio principles, and other topics. Kids as young a 5 years have passed the test, along with many blind and deaf people.
Technician is the first license and covers the basics, and next is General class. By the time you make it to the final test, which is Extra class, you will have an in depth understanding of all the above and more, and will be building and possibly designing your own circuits as long as you have been playing and practicing which I believe you will be.
Also, there is a lot of camaraderie, friendship, and support in the amateur world, so there will always be another ham that can help you with a problem no matter how advanced or complex since there are many electronics engineers that are also hams.
Also, once you get your license (ticket) you will have the ability to communicate with others when mother nature rips through your area tearing out power, phones, internet, telephone poles, etc from your normal life. You could be the only link in your neighborhood to the outside world, or be helping others in that situation such as Katrina. Even though I am in N.H., I took a report of a family trapped on a roof in the affected area and reported this to the authorities in LA over the phone.
A couple of great references to have is the American Radio Relay League's (ARRL) Hints and Kinks series which starts with the basics such a how a resistor, capacitors, etc works and uses them in a simple circuit so it can be understood. There are hundreds of these.
You will also want to pick up a copy of the ARRL's Handbook which is a complete reference for almost everything electronics, and almost everything radio too. The later versions include a CD for easier reference.
You ask what a transformer is. This item is coils of wire wrapped around of some type of iron core that converts the input voltage to another higher or lower voltage. If you needed a power supply for a 12 volt device that might work in your car, you would use 1/10th the number of turns in the secondary as compared to the primary turns. This is a very simple explanation BTW, as there is a lot more to know about them.
Now, in the case of the disposable camera, I assume you are talking about how the flash works, and that actually doesn't use a transformer but what they call a charge pump to charge the capacitor that releases its energy to make the strobe tube fire. http://en.wikipedia.org/wiki/Charge_pump
**WARNING** the voltages in a strobe tube are lethal. DO NOT disassemble a flash, strobe pack, etc until you understand them, and are familiar with them and their safety. http://en.wikipedia.org/wiki/Flashtube
Flashes use voltages anywhere between 250 and 5000 volts, and 30 volts is enough to kill anyone.