The tongue like a sharp knife...Kills without drawing blood.
First of all please remember, you can hurt yourself doing this. You know, kind of like "don't run with scissors". If you are unsure of or scared of trying to partake in such activity, you can take the knife to a professional for fixin' up.
Sharpening a knife can be a two step process, depending on how badly dulled the blade is. If the knife can't, as an example, cut a tomato, but it crushes it instead, it definitely is in need of a sharpening. If the blade is really dull, you have to hone it first. Honing may not always be a necessity, but if you need to hone the knife, you will have to take care of that part first.
In order to hone or sharpen a knife, you will need a sharpening stone. For the honing, the stone will have to be coarser than it would need to be for sharpening, in order to put the edge back on the blade. In addition, the stone needs to be harder than the steel of your knife. A harder steel knife, there can be different hardnesses, will take longer to sharpen, but keep it's edge longer. It is possible to get other types of sharpening tools, like a X-shaped tool, where you insert the knife into a groove and drag it back out or a ceramic sharpener, with a long, thin, stick shape, kind of like what you see sushi chefs use when they sharpen a knife before using it. In most cases, I think the stone will be best. With the stone, you can get one that has different types of coarseness, one side for honing and the other for the finer sharpening. A highly recommended stone is the Arkansas stone, a very hard, very fine, stone from, well, Arkansas, of course.
Take your honing/sharpening stone and place it flat on a surface that will prevent it from slipping, like a rubber mat. Wet the stone thoroughly, with either water or oil. There are honing oils, but mineral oil will work fine. Note that once you use oil on the stone, you won't be able to use water for the stone. With the stone ready, you can place your knife to the stone.
Place the knife on the stone with the blade facing away from you. Obviously, you aren't gonna place it flat against the stone, but it should be at an angle between 18 and 22°. The harder the knife will be used, the wider the angle should be to the stone, i.e. if the knife will be used outdoors on wood, rope, etc., it should be closer to 22°. To have a general idea of the angle range, you could put your thumb at the back of the knife and lay your thumb against the stone. There are guides you can purchase, or I have seen an example where someone stuck an alligator clip on the back of the knife and used it for the guide.
Once you have your proper angle, you need to maintain it throughout your sharpening. With the knife in place, you push the knife away from you, leading with the blade edge, using a constant pressure on the knife as it slides across the stone's surface. At the end of your stroke, turn the knife over by it's back side, not the blade so that you don't scrape it against the stone, and now drag it across the stone again, blade side first again. This should be other side of the blade than what you just started with and now you are pulling the blade towards you. Repeat this motion 10 to 15 times with the same number of strokes for each side. This will take care of sharpening the knife's blade, but you can still fine tune the edge with a strop.
Before I mention using the strop, as far as honing is concerned, you would follow the same steps as sharpening, just with the rough side of the stone. Now, a strop is one of those big leather straps you see barbers use to add a little more edge to their straight razors. For those of you fellas that still go to barbers for your hair maintainance needs. If you are one of them new fangled types of fellas that goes to a "hair dresser", then you don't need to read this. Anyway, if you are wanting to take that extra step with your knife, you will need a strop, avoid that barber's strop cause using the curved knife edge on the strop will make it useless for the straight edge razor when that razor needs to be sharpened again.
With your strop firmly attached to something and flat, put the knife to the strop and drag it across in a manner opposite to what you did with the stone, with the back end leading and the blade following. Like the sharpening with the stone, make the same number of strokes on each side and at the end of each stroke, turn the knife over on it's back side. Continue until your knife is at a satisfactory sharpness. One test is to hold a leaf of paper up and cut the paper by just running the paper against the knife's blade.
The process just described works well for knifes that have a plain edge, not a serrated edge. Such knives require a little more effort and won't work as well with a stone, in this case you will want want a ceramic/steel sharpener or X-shaped sharpener, so that you can work into the serrations.