How should I run CAT6 wiring from one side of my house to the other?
Use Cat5e (good for 1GbE) unless you have a spectacular reason to use Cat6a (10GbE)*. Cat6 is essentially a deprecated spec, nobody should be using it for new installations.
They make structured cabling conduit. It's cheaper than the PVC electrical conduit. PVC works great if you need something rigid. Copper would be incredibly expensive and complete overkill.
Your local hardware store probably has a book on retrofit electrical and structured wiring. It would be a good buy/read for someone who hasn't done wiring before. 
Consider using your air ducts to run the wires. It's really not a good idea as you wont be able to clean the ducts anymore, but people do it when in a bind.


*Consumer computers probably wont come with 10GbE NICs for another decade. There's very little demand and the technology is incredibly expensive (compared to 1GbE). Most Internet connections are still &lt;10Mb anyway, so 1GbE is already 100x faster than the primary use case.