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There are three basic problems that lead to a drifting cut.
- The Setup: If your saw is not properly set/sharpened it won't cut straight. The teeth of a hand saw are set (bent away from the centerline in alternating directions) so the effective cutting surface is just slightly larger than the body of the saw. That way as the cut deepens the body is less likely to bind in the piece. If the net affect of the set favors one side or the other it will "drift" in that direction. Likewise in the case of a crosscut saw, the teeth are filed in opposing angles to help sheer the fibers as they cut to prevent chip out. If the sum of the left facing angles is greater than the right it will tend to wander off in the that direction, although generally not with as much exaggeration as if the set is bad.
- Technique: Believe it or not there are some techniques to using a handsaw beyond just pushing it back and forth. Even if you're just roughly sizing a piece it's still worth striking a line for both your long and short direction so you can see where you're going. But more importantly than that is how you pursue the line. If you attack the cut at 90 degree angles you're always fighting with the entire length or depth of the saw (depending on if it's a rip or crosscut). You have much more control if you shoot for cutting angle that ranges from aprx 5 to 30 degrees to the two dimension of you're cut. Start out with your saw basically flat to the face and make a few inches of cut. In this mode you'll only be engaging the teeth of the saw which makes controlling the direction of cut much easier. Once this starts to feel akward, switch to cutting deeper instead of "forward" until the angle of bottom of the cut rougly represents the hypotonuse created by the long and short dimension of the cut, being careful to keep on your short line. Now rotate back to cutting flat and repeat. If you have a cut that needs to be really precise, replace the pencil line with a knife wall (a knifed line deepened with a chisel). The shoulder of the knife wall will act as a bearing surface and, to a certain degree, guide your cut automatically.
- Tension: In the case of the frame saws (coping, fret, and bow saws) poor tension of the blade, specifically a lack there of, will cause all manner of problems. Also, at least in the case of my coping saw, the blade can be installed in either direction, which means it can be accidentaly set up to cut on the push instead of the pull. I would be embarrassed to tell you how I know this :)