This has been discussed many times on this site and maybe even a few times on Server Fault.

Step 1: The plan

Come up with a plan - how many drops per room? Where will you terminate all the wires back to? Are there clear path's from floor to floor via the walls? ie: is there an empty part of the wall on the first floor but not on the 2nd floor? Do interior walls line up from floor to floor? Running wire through exterior walls will be more difficult as they contain insulation.

Step 2: Find the framing

Get a damn good stud finder and a pencil and start marking studs and measuring from exterior walls to make sure you end up strait as you go from floor to floor. Do this in the basement also - find the floor joist for where your drops come through in the basement and mark them.

Step 3: Execute

Assuming all the paths are clear, start cutting / drilling. Use a 6 foot flexible drill bit. Cut a box on the first floor for your first set of drops. Drill down through that into the basement.

Directly above this box, cut an access hole about 6-8 inches from the ceiling big enough to get the drill bit through it - about 4 or 5 inches square (square will be easier to patch later on)

Goto the 2nd floor - cut your next box for your 2nd set of drops. Its easier to fish wire down then up, so I would start on the 1st floor, put the fish tape into the access hole at the ceiling, find it in the box hole on the 2nd floor, attach your 4 lines to it and pull the fish tape down. On the 1st floor, fish the tape up from the box hole to the access hole, connect the lines to the tape and pull down. And again, goto the basement, find the hole, fish the tape up to the box hole on the first floor, attach the lines and pull down.

Now that your in the basement, run the lines to your network closet - leave enough extra wire per drop to make sure everything reaches - rinse repeat.

When your all done, everything punched down, start patching your drywall holes.

You can do this by yourself but would be a lot easier with 2 people Lots of time and multiple boxes of cable. 1 box of 1000 feet wont help you, you'll be fishing each line individually and if you precut them, you may waste wire; get some small boxes of 250-500 ft and run all 4 lines at 1 time.

Equipment required:

• Drill
• Flexible drill bit
• Utility knife
• Fish tape
• Electrical tape (to attach network cable to fish tape)
• A TON of patience.

If this is a cable TV wire, your best solution is to get it re-run properly by the cable TV company. Unfortunately, that sometimes can only be arranged by figuring out when it would be least inconvenient to you to have the cable out for a while and then running over it with the mower, etc - at least in my experience they are good at coming to fix stuff, bad at fixing it when it ain't broke. Your Mileage May Vary.

Now, if you'd like it run in conduit this time, they are not going to go there, but they generally won't mind if you do, so you might run the conduit (presumably in the "not all the way around the house direction" unless there's some good reason for that) before you mow the lawn and hit the improperly installed cable. If you can avoid most of the around the house run by having an inside the basement run, go ahead and run that cable (they won't do inside cable work, for the most part) and have it handy for connecting to their new cable.

I had a ridiculous replacement cable run when our old one filled up with ice at a bad connector, and for obvious and understandable reasons the installer did not want to run a new one where the old one was going along the icy roof, so he tossed one over the edge and down the outside of the building to the ground. That installer suggested calling back when things were warmer to have a better one placed, or getting an inside cable run and calling back to avoid the roof entirely. I had the inside cable run, called back, and they would not come switch it over; so it sat for several years until I next had a problem with the cable service they would come fix, at which point the installer was happy to switch to the inside cable. I did not actually attack the dubious cable, but I considered it...