If this is a multi-story house, first and foremost, you need to figure out how you're going to get from one floor to the other. This is often hairy. You can wire second floor drops by going down from the attic, and you can wire first floor drops by going up from the basement (unless the basement is finished, then it's a lot more painful!). But getting from attic to basement... that's going to be a lot trickier.
The first place to look is for your heating plenum, which would carry air ducts from basement to attic. The main thing you need to be careful of when running anything in the plenum is FIRE safety. I would strongly suggest that if you choose to run through the plenum, you get plenum-rated cable (CMP), run it inside a closed conduit pipe, and to shove some rock wool or other fire retardant material to fill the ends of the pipe when done. This is a bit on the paranoid side, but think about it: do you want an express path for fire in the basement to climb into your attic?
Anyway, the problem with plenums, as well as with trying to run in a wall from one floor to the next, is that there are usually solid barriers at the floor/ceiling level. So for example, your plenum often has floorboard material in its volume and cut outs only just big enough for the ducts, with metal plates covering up any excess. Then they shove in fire retardant material. For fire code reasons, the plenum often has such barriers at every floor, so there would be a floorboard+metal barrier between basement and 1st floor, another betwen 1st floor and 2nd floor, and another between 2nd floor and attic. The first and third of those aren't hard to cut into if you have access to the attic and basement, but the middle one will be a huge pain because it'll be maybe 9 to 11 feet away from the points where you could access it. You'll probably have to cut into the drywall thereabouts and patch when done. If you want to try going through a wall from attic to basement, the game is very similar to what I just described for the plenum, except that you'll mostly be going through wood, BUT you have to watch out for walls that don't actually align, wires such as power lines in the walls, and insulation on outside walls.
Moral of this story? For getting from basement to attic, if you don't know what you're doing, it might be worth it to get an electrician to do it. They're used to it.
Now, the drops are a ton easier. What I would suggest you do is go down to your local Home Depot and get the blue conduit tube and the PVC boxes that can be snapped together with the tube. Get a drill bit for cutting out holes that's a little bit bigger than the tube's outer diameter. Also get a bunch of stuff for patching drywall, you're going to be doing a lot of that, spackle, touch-up paint, sanding blocks, etc.
First thing you need to do is to try hard to figure out where the actual electrical power wires in your walls are. They're pretty much either going to be straight horizontal (outlet box to outlet box) or vertical (attic/basement to outlet box, OR up/down to a switch). The main ways you can try to figure this out are to take off the electrical faceplates and look around the wiring boxes for how things enter and leave, take a look above the wall in the attic and below the wall in the basement to see where vertical runs are, and toner sets. There are different kinds of toners you'd use for current-carrying power lines; the ones for finding circuit breakers work okay for this. (you also might want a low-voltage toner for the wiring job, while technically possible there are all sorts of things you have to be careful of if trying to use them on power wiring and so if you have to ask... don't try that!).
This assumes the original electrician was pretty neat about the job, which luckily is common (it's also easy to do it this way). The key here is that you want to avoid current-carrying power wires like the plague when running low-voltage wires. At the least, they're a bit bad for signal quality, at the most, you can electrocute yourself and/or mess up your electrical wiring if you screw up while working near power wires. Oh, and figure out what's on what breaker, so you can turn off the electricity near the wall you're working in!
Okay, so now that you have a pretty good idea of where the power wires are, it's time to tear up your wall.
Find a spot you want a wall box. Make sure there's no electrical boxes or wires really close by. If you don't mind appearances, you could try putting your network boxes about 6" higher than the level of the electrical outlets on 2nd floor runs and 6" lower on basement runs, this makes it a lot easier to avoid the horizontal power lines. Now, find the closest stud with your trusty stud finder, and figure out which side of the stud you want the box on. Move out from the stud a little bit and oh so carefully cut into the drywall. If you feel like you're cutting into something that's not drywall -- stud, wire, pipe, or who knows -- STOP! If all is well, though, you should be able to cut a small hole, enough to just barely shove the box through. But don't do that yet! Go to the attic or basement end, locate the same stud you were working next to (a way to do so would be to measure from a landmark in the room and then again at basement/attic, but be careful as this is can be very deceiving). Move to the same side of that stud and drill a small hole down. Hopefully you should be able to see light through. Tie a small weight to a line (fishing line works great, or you could use fish tape here), and drop it down the hole... and see if you can find it back in the room through the hole you cut in the drywall. This step is important, make sure you've got the hole in the drywall and the hole in the top/bottom of the wall in rough alignment before you make those holes bigger!
Okay, NOW drill out the hole up top/bottom and shove the conduit pipe down through it. Snap the snap-thread connector onto the end of the conduit, attach the box to the stud (uhhh... I don't know a good way to do this retrofit, I've always done it pre-drywall... talk to the friendly Home Depot guys about this!), stick the snap-thread connector into the hole in the box, screw the nut over the threads to hold it in place... and you have a box and conduit. Yaaay!
Now pull wire through the conduit, and make sure you've got a good bit of extra wire. Do your faceplate terminations in the room and on the other end of the wires, then carefully pull the wires back through the conduit, thus "sucking" the faceplate into the wall box. You'll probably have to finger-feed some wires back into the conduit and play with it to get it all in place. I've found that it's easier to have almost no slack in the boxes and some slack in the attic or basement.
For a retrofit job, my expectation is that you're going to have a lot of trouble getting from attic to basement, so you're probably best off doing as many riser runs as you can manage and then putting a patch panel and/or switch in both attic and basement and interconnecting them on the risers. If you don't have electricity in your attic, that would definitely make putting a switch up there more challenging. Oh, and be very careful putting any live equipment into your attic, again the whole fire safety thing. But anyway, if you have ultimate flexibility you would want to home-run every drop to one central patch panel, but if you can only get a couple of cables basement to attic, you need to make the most of those cables.
Other notes... the quality of tools you have makes a huge difference. But if this is the one wiring job you think you'll ever do, then it probably isn't worth spending lots of $$ on tools. This is again where you need to compare with hiring a professional to do some of the work, because they've got tools and have done it before, while you haven't. For harder parts of the job like the risers, it might really be worth it to just pay somebody. Still, it's a great experience to have done it yourself and learned, I don't want to discourage, only to make sure you do what's sane.
I've done a good bit of wiring in my time but am solidly an amateur, so don't take any of this as gospel, just my advice based on what I've done. Make good friends with the electrical and drywall guys at your local Home Depot and they'll give you lots of free ideas and hints about how to do that stuff.