The best ways are running it through an attic if possible. I have run the cable into a closet and just drilled a hole in the ceiling to get it up there if the walls aren't easily fishable.....take a look at this video: http://www.youtube.com/watch?v=e2--l-YX1HU
Big topic, and lots of planning and decisions. The guide I linked to should get you started. Need to figure out if you want to run the wire through the basement, the attic, the baseboard, or somewhere else.
How far away is the computer from the modem, and how many walls in the way? Is running a cable through the attic a possibility? Can you put the modem in a closet?
I would think about doing this with WiFi or Powerline which will be easier for you.
The best ways are running it through an attic if possible. I have run the cable into a closet and just drilled a hole in the ceiling to get it up there if the walls aren't easily fishable.....take a look at this video: http://www.youtube.com/watch?v=e2--l-YX1HU