How do I run ethernet cable through a wall cavity?
As others have mentioned, there may or may not be stuff in the wall obstructing your plan.  But most likely not (insulation it the most likely, but should not stop you).  Find an area between the studs and cut a hole in the wall where your box will go as other have described.  Then drill a 3/4" - 1" hole in top plate within the same stud cavity.  That's the easy part. 

To actually fish the wire (up or down), you really should get steel fish tape.  I spent so many years fishing wire without this, and once I discovered them, I realized I could have saved so much time.  It is a steel wire that rolls up but does not bend left to right, so you can put it up or down the cavity (down would probably be easier as you can stick your hand in the hole too grab it).  One you have it pulled through, attach your wire to the end, and pull it back up.  Believe, this will well worth the $7.99 you will spend.



I have also used a contraption that gets attached to the fish tape that is like those old Chinese finger traps you probably played with as a kid.  It's a wire mesh that you put you wire in, and then locks on to your fish tape.  As you pull, it gets tighter on the wire so it will not disconnect in the wall.  Before I had one of these, sometimes the wire would disconnect from the fish tape in the wall and you would have to start over.  I could not find a link for this, but it is sold in the big box stores right by the steel fish tape in the electrical section.

Good luck!