Joblot, the reason that it is ok to use a sterling style sharpener on a cheap knife is that after a few uses and the knife edge has been destroyed you can then go out and buy a good knife. The carbide insert sharpeners remove far more metal in one pass than any of the other sharpeners listed in this thread and it also wears the edge unevenly. Where i used to work we sharpened knives for customers and i could always tell a knife that had been used with a pull though sharpener, personally i would not use one on a cheap knife. The DMT and the ceramic sharpeners are the way to go, once you learn how the DMT will be the one you reach for.

If you are looking for instruction do you have a hardware store, sporting goods or cutlery shop near you that offers knife sharpening? If there is take in a couple of knives that need sharpening and let them have a go at it then ask how to keep the edge on your knife and most likely you will get a demonstration of how to correctly sharpen a knife. Starting with a sharp knife makes it easier to keep a sharp edge and you can see after a few strokes on a sharpener whether or not you have made your edge less sharp. If you are learning on a very dull knife you may be doing everything correctly but you will most likely get discouraged because you are not seeing any results from your labor. More than once i had someone come in and say, can you sharpen this, I have tried everything and nothing works. When i would ask what they had done they more often than not were doing the right thing (or close enough to get an edge that would cut) but the edge was so far gone that they would give up long before hand sharpening would produce any results. HTH and remember to practice.