For Sharpening, I would try and find yourself a cheap two sided stone(course/fine). You could spend more, and get diamond hone, or 10 different grit stone, but for now on a limited budget, a two sided stone should work fine.
Everyone does it different so here are the two most popular ways:
1) Make slicing motions over the stone, like you are trying to take very thin slices off the top of the stone.
2) Make circular motions over the stone, still like taking thin slices off, but do it with small circular motions. (This is how I do it, seems to take the metal off faster)
Which ever method you choose, you want to make sure that the edge is laying flat on the stone, so you don't change the angle of you edge. Depending on how dull your knife is, you can start on the course side, or if it just needs a touch up, just use the fine side.
Work both sides of your edge equally while periodically checking for a burr. When you feel a burr, keep working the one side until you get that burr the entire length of you knife, then switch to the other side, and work it until you get another burr the entire length of your knife.
After you've gotten a burr on both sides, tilt you knife up slightly to raise the angle, and make one or two lite passes to get rid of the burr.
If you started on the coarse stone, repeat on the fine stone. If you started on the fine stone, then you're done.
If you want to refine your edge a little more, you can strop it on a piece of leather. The back of you're belt will do if you don't have leather laying around, that is if you were a leather belt that has the course side of the leather on it. To strop, lay the edge flat on the leather and drag the edge, instead of pushing it like you did on the stones. Do this several times on both sides of your knife, to give it that little extra.
If you are not sure if you want to practice your sharpening on your precious leek, then I suggest you pick up a Mora #510 and practice on that. Why?? Because it is a very cheap knife($9), so if you screw it up it won't hurt your wallet, and because it only has one edge bevel which is very wide, so it will be easy to know that your edge is flat on the stone. This will get you used to holding your knife at the right angle and getting the feel for how it all works. Plus, now you'll have a darn good belt knife as well.
You can buy the Mora #510 from here:
http://ragweedforge.com/SwedishKnifeCatalog.html (scroll down until you get to #510, it has a red handle)
P.S. A tip to make sure you are holding your leek at the right angle is to lay the knife on the stone at too low of an angle so the edge isn't touching the stone, then look down the knife from the tip, and start rotating the knife up until you see the edge touch the stone, that is the angle you want to keep it at. Check that you are using the right angle periodically, and
TAKE YOUR TIME.
I hope this helps, for more information on knife sharpening and "Burrs", check out this link:
http://forums.egullet.org/index.php?showtopic=26036 (scroll down to 'section four: Sharpening basics' for info on what the burr is and how to detect it.)