Well the first thing you’ll need is a sharpening stone.

I like these stones for starting with, they have two different grades, coarse and medium and they’re cheap (these cost A$3). Which is a good thing as they wear out, especially if you have to sharpen very blunt knives often (which I do as mine get touched up frequently but everyone else doesn’t want to bother me so I get very blunt knives to sharpen). Ideally you’ll want another stone that is very fine, this one will last (mine came from my great grandmother’s place) so it’s worth spending money on a good stone.
Next you need lubrication or that stone will wear out quickly, you can use water but I prefer dishwashing liquid. Place the stone on a secure surface and provide lubrication. Start with the knife tip at the stone’s edge closest to you and push the blade along and across the stone so that with a small knife the entire blade has crossed the stone at a constant angle (a larger knife can be done in sections). This angle is easiest worked out with a sharp blade until you’re familiar with what the angle should be. Basically if the angle is too high the blade will dig in to the stone so move just back from that angle and you’ve got it right.
After one stroke on one side repeat on the other side and continue swapping sides. Once you feel that grade of stone has done as much as it can you move onto the next grade of stone and repeat. The only reason to do one side more than the other is to even a blade out if some one has decided to sharpen one side first. Once sharpened it should cut a held piece of paper cleanly with no effort and no snags.
This how I sharpen blades some people prefer to work the blade in circles across the stone, each to their own.