Buy in-wall cat-6 in a bulk 1000 foot box. Put a patch panel near where you want your router. Terminate your in-wall cable to the patch panel, and keystones where you want your outlets. Here's a good video on wiring keystones.
You'll use the same technique and punch down tool to connect the other end at the patch panel. Use patch cables to connect the patch panel to the ports in your router, or to a switch (8-port—ok, 16-port—better, 24-port—much better) with one port patched to your router.
Read up on the requirements to run cat-6 in walls, paying attention to radius, proximity to line voltage, etc.
I don't have any links handy, but there's tons of info available.