You can't, it's a fundamental aspect of quantum mechanics (measuring any entangled system collapses it because you've forced the system into a state by measuring it).

The idea is that you structure the QC system such that the computation is done using entangled states, but when it comes to measuring the qubits (to get the result of the computation) the state is such that you'll get meaningful results. This means the quantum state at the end of the calculation would ideally be along whatever axes you're measuring, so you get the same answer 100% of the time.

OK but this implies that you'll have to know beforehand what a result will look like. Which kind of beats the purpose of a general purpose computational device.

No it doesn't. You know that the result of the computation for an individual qubit will be either 0 or 1 (otherwise it would be useless -- measuring only gives you one bit of information), so you construct the system such that after the computation is done each qubit will be aligned with the |+z> or whatever axis. The key point is that you have to be clever about how you construct the system for a given QC algorithm, not that you cannot do arbitrary computations using the system.

OK but we're back on square one. If you can't read info from qbits without breaking the state of the whole freaking system then what exactly is that you reading? Doesn't the alignment info collapses superposition?

You do "break the state of the whole freaking system". Once you've read the output, you're done. You have to set up your initial state again and run the computation from scratch.

You design the algorithm so that it collapses the state into the right result.

You read the 'probability the qbit is one' by running multiple times and doing statistics.

I found an explanation of schor's algorithm by my colleagues quite helpful. In my experience math seems to be more useful here than computing science.