The bow is in it's most basic form a very simple construction. It doesn't need to be more than a stick strung with a cord. It will essentially be effective for killing small game on short range. Two methods for making such a bow will be described here.
This method is the quickest and was the only way I made bows until I was about 12 years old. Conifers are best for this type of bow as they are "drier" and snappier in their fresh state. I prefer juniper (Juniperus communis).
Chose a relatively straight tree, chop it down, break off the top and the branches and string it up. That is all. You know have an acceptable, but assymetrical bow. The bow will increase in strength over the days as it dries up and will eventually become so dry that it becomes brittle. But then it will already have served you for weeks, and you can easily make a new one.
A suggested improvement on this type of bow is to split or carve off quite a lot of material from the centre and down on the belly side of the thickest limb. This way you will achieve a more symmetrical bow. Symmetrical bows are easier to shoot and more efficient. The reason why I didn't do that on this particular bow was due to lack of time.
The second method is better if all you have available to you is hardwood or the conifers are so thin, thick or brittle that they arn't usable for the other type of bow. This method also give you a longer lasting bow, as it will not become too dry.
Choose a wood that can stand a lot of abuse. Rowan, oak and elm are good candidates. Choose a straight tree with no branches and a diametre a little thicker than you think you need to achieve the draw-weight you are looking for.
Strip off the bark and work the bow on the belly and the sides on the thicker end to get a more symmetric bow. Floor tiller to test the bending strenght on both sides.
When you have the symmetry you want, cut notches in the ends of the bow and dry it by the fire. If there are any bends you can straighten them out at the same time. This will take the rest of the day, but it will still take a lot shorter time than if you were using conventional methods. When the bow is no longer sluggish to shoot, but snaps back quickly, the water content is reduced sufficiently for it to be usable. It will continue to loose moisture over a long period of time and become stiffer and stiffer, but it is essentially finished at this point. Sorry I don't have a photo of a finished bow of this type. Couldn't find it.
Remember that it doesn't matter so much how your bow is like. Accuracy lie in your aim and your arrow.