How are Quantum Computers supposed to work?

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I know regular computers, essentially, read a 1 or 0 state and can store and compute so many of them so as to mimic analog(real word) information.

Are Qbits like analog bits? Would they in theory be able to take analog information and make an analog computation? How would you program such a computer.

I've done some reading on quantum computers over the years, I'm just trying to get it in my own words.

They can do in one operation what takes a lot of operations to do on traditional computer.
For example they can do trigonometry and using the result immediately for further results.
The problem with quantum computers is the errors. It is not perfect like traditional computers.

See http://en.wikipedia.org/wiki/Qubit
http://en.wikipedia.org/wiki/Quantum_computer

I only knew that quantum computers were susceptible to decoherence, which causes all the entanglements to break off and everything just to mess itself up. Do quantum computers make errors because of the uncertainty principle, too, or is this just me and my lack of training in physics being wrong again?

I have read about error problem with quantum computers where they used traditional computers to verify the results. But it is possible it was about decoherence, I don't remember the article well.