I have a cylinder charged along its length, and a charged wire inside it. The electric field inside the conductor is zero, but how is it when I have a charged wire inside it?
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If you are dealing with electrostatic you are interested only in static field. When external field acts on a conductor the free charges inside it move, creating in the surface of the cylinder a density charge. This surface density create an electric field that has opposite direction and the same strength of the external field, inside the conductor. Then the sum of the two fields inside the conductor is zero.
There is certainly a transient time where the charges move freely, adjusting in a way to cancel the external field. Since we are dealing with electrostatic we ignore this time and we look only at the final state of the system, after this time. The time depends on the material and it's related to conductivity and permittivity.
Mark_Bell
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The charged wire will attract an equal but opposite charge to the inside surface of the cylinder. If it runs down the center of the cylinder, you have enough symmetry to find the fields, inside and out, using Gauss's law. Otherwise, the situation gets complicated.
R.W. Bird
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