There are lots of gadgets to sharpen knives. Why? Because most folks don't know how to do it without the gismos so the marginal improvement the thingamabobs do seems like magic.
To do it right you need three things: your blunt knife (derp!), a two sided sharpening stone. a sharpening steel. There are alternatives that work almost as good like I have often sharpened a blade using wet and dry sandpaper.
So, firstly your abrasive, Use a 2 sided carborundum (silicon carbide) sharpening stone. Place it flat on a suitable surface or hold it in your hand.
Place the side of the blade against the rough side of the stone. Lift the back of the blade just off the stone. The correct angle is when the centre of the blade is 11 degrees to the surface of the stone. Work the blade and stone against each other being very careful to keep the blades angle constant at all times. It does not matter which way you work the blade. Round and round, back at forth or along the blade they will all work in this stage of the process. This stage is the most labor intensive but don't worry: the other stages are much shorter and the whole process will be quicker next time.
As you remove metal from the blade there is also the wearing away of the carborundum. These worn, gritty substances wear down the edge you are trying to create. The standard solution is to wet the abrasive with oil and such. I recommend not using oil or kerosene as it allows the grime to work its way into the pores of the abrasive. I use a steady stream of water or regular dunking of the stone in water. You want to wash away the grime not lubricate the abrasive.
The most important thing in this stage of the process is to keep the blade at 11 degrees. Any less and you are wasting your time and trying to remove, very slowly, a large amount of metal which is the side of your blade. Any more and you will be rounding the edge which will compound in the later stages of sharpening to a stumpy, rounded edge instead of the fine, thin edge you are after.
Do not swap over to the other side of the blade until you can feel a burr along the entire edge. This burr is felt on the non honed side of the edge and feels like a find wire sitting along the edge. To feel the burr run your finger from the side of the blade to the edge and off the edge. If you run your finger along the edge or from the edge to the side you risk breaking the burr off prematurely, cutting yourself and imbedding the burr in your finger. Metal splinters are not what we are trying to achieve here.
When you can feel the burr along the entire length of the edge it is time to hone the other side of the blade at 11 degrees. It is important to not go above 11 degrees even if you feel that you could get rid of the burr faster this way. Stay at 11 degrees! Keep honing on this side until you can feel the burr along the length of the other side of the edge. You should have spent this entire time on the coarse side of the stone (or a sheet of 80 grit wet and dry carborundum paper laid flat on a flat hard surface).
Now for the easy bit where we are going to be really careful and gentle! Switch to the fine side of the stone (or switch to 240 grit or finer paper) and carefully apply the burr side of the edge to the abrasive at 23 degrees. Keeping it at this angle move the blade in the direction of the edge (edge first) as if you were shaving the stone. Only apply gentle pressure and lift the edge between strokes for two strokes only. Turn over the blade and repeat the two gentle strokes on the other side.
Your blade is now SHARP! Try and shave some hairs from the back of your wrist.
To get sharper than this can try 1) use a harder metal for your blade, 2) a finer smooth abrasive like jewelers rouge on a sheet of glass, 3) a harder surface for the smooth abrasive like a diamond hone.
Commercial razor blades are sharpened either using electroerosion or ultrasonic honing against a hard surface like glass in a jeweler's rouge suspension.
