OK, I'll try to answer again since you're looking for a
sharp edge. It doesn't really matter if you draw the edge towards you or push it away from you but, sharpening edged tools for decades, I've come to find it easier to maintain a bevel by pushing the blade or using a "figure eight" motion. The important thing when trying get a sharp edge is not to rock the blade. You need to lock the position of the blade at the correct angle. Only the flattened bevel should touch the stone and you want to wear this away as evenly as possible. Sharpening edged tools by hand is easy in theory but it takes practice; the steadiness of your hand position is of utmost importance. Here's another tip: you can lubricate your stone with water and a little mild soap instead of the usual honing oils; this way you don't get oil on your fingertips, hands, mouthpiece, and reed.
I did a search and found
THIS page which goes into great detail.