The field is called Electrical Engineering or EE for short. As mentioned, you will need the basics in order to further explore the solid state. Read up on Ohms Law and the like. Discrete components such as transistors and capacitors are the building blocks for everything. CPU's are nothing more that billions of transistors, and RAM is nothing more than sophisticated latch registers.
The books Goon provided a link to from Forest Mims are excellent for understanding digital and analog circuits. If you want hands on learning, go to RadioShack and get the Electronics Learning Lab, that's what I started with back in the day and is an excellent guide and source.
Once you know the basics, you can move onto microcontrollers. RadioShack should be stalking Arduinos and/or Parallax BasicStamps now. You can also get PICs which are pretty popular.
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If you need to make something relating microcontrollers and microprocessors Learn ASM. Assembly is necessary to interface with various chips and Ports.
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No. You can code with C and achieve the same things in a language much easier than ASM. Except for Parallax, that is done with PBASIC. You can go the Arduino route also, and use an abstracted layer to code the chip with the IDE and bootloader which is more forgiving to beginners.
You wont be able to understand everything inside a computer for no less than 15 years of studying. You will have to know stuff like UART converters, ins and outs or driver chips such as video output, I2C busses, wifi radios, DACs and ADCs, etc...
You can also venture into the world of FPGA's, but knowing digital logic and gate configuration are a requirement. A lot of colleges are teaching FPGA instead of microcontrollers.
I will also be posting tutorials on this subject when I get the time (new job), ranging from wireless inductance charging to home automation.
