For a question so open ended there is no good concise answer. You could do a degree in computer science and still want to know more.
My suggestion would be that if you want to get answers here you try and come with more specific questions for people to answer, or that you go and do some serious reading. Wikipedia might be good for starters but I think you'd quickly find yourself wanting some decent books.
The question is, which layer do you want to start looking at? Computer science is so deep a field that nobody would get anywhere if they tried to understand every part of a system all at once; they have to be viewed as layers of abstractions. At each layer you forget about the implementation of the layers above and below you and think only in terms of how they behave. If you want to go bottom up, take a look into digital electronics (try combinatorial and sequential logic, then look into functional units such as adders). From there you can get to the ideas behind the fundamentals of processor design. You could delve into a middle layer and have a look at some MIPs assembly code and perhaps try some with the
PCSPIM simulator. A slightly higher level entry point that might be interesting is the Wikipedia article on call stacks:
http://en.wikipedia.org/wiki/Call_stack. You're then getting to the point of wanting to look at operating system design, memory models, processor design, and more.
For the lower level layers you might be able to get away with learning through reading. Higher level stuff you really are best off learning about through doing (i.e. having a go at programming things to see that the layers fit together).
With regard to your question about displays and bits, you might find the Wikipedia article on the OSI layers informative:
http://en.wikipedia.org/wiki/OSI_protocols.