In the right hands, a tenon saw cuts accurately and quickly. Tenon saws aren't as common as they once were, largely owing to the prevalence of inexpensive Japanese pull saws that can do the same job with less effort and even more accuracy.
Crosscuts
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Mark the cut line with a carpenter's square and a sharp pencil. To get the most accurate cut, clamp the wood to your workbench with C-clamps so you can hold the saw with both hands.
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Grip the saw handle with all but your index finger wrapped around it. Your index finger should point forward to stabilize the saw during the cut.
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Align the blade with the cut line and score the wood by making a single cut by moving the saw in a forward direction. Tenon saws, like most Western handsaws, cut on the push stroke. Making an accurate score is essential -- it determines the accuracy of the cut in general.
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Saw through the score line, keeping the blade longitudinally and laterally perpendicular to the wood surface. With a well-maintained, sharp saw, you should be able to cut through nominal 1-inch lumber in about seven or eight strokes. Use your free hand to push down on the blade and provide extra cutting weight.
Longitudinal Cuts
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Draw the cut lines for a tenon or notch, using a square and pencil. Draw perpendicular lines on the end on the wood to make it easier to align the saw. Support the wood upright in a vise.
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Position the saw on the end of the wood, over the cut line. Make a single forward cut to score the wood.
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Cut along the line, using your free hand to guide the blade and keep it straight. The first few strokes are the most important -- if you angle the saw, the notch or tenon won't be straight. Once the saw has sunk about 1/2 inch into the wood, the kerf should keep it straight.