From the wrist, not the arm
The chasen should move from a relaxed wrist with a quick back and forth action. A stiff arm produces a slow, splashy whisk that incorporates large bubbles instead of fine ones. Hold the handle with a light grip, around the lower third, so the tines can flex naturally as they pass through the tea.
W or M pattern
Most teachers describe the path as a W or M shape across the bowl rather than a circle. Circular stirring tends to push powder around without breaking up clumps or building foam. A linear back and forth pattern, kept fast and shallow, gives the bubbles time to subdivide as they pass through the tines.
Where the tines sit
Keep the tines a millimeter or two above the bottom of the chawan rather than scraping it. Scraping abrades the bamboo and produces drag without adding foam. Saponin extraction in matcha peaks near 70 degrees Celsius, so a warm bowl and water in the 70 to 75 degree range gives the chasen the best chance to lift fine, stable foam.
Coarse to fine
Foam tends to start large and chaotic, then refine as you keep whisking. Once the surface is fully covered, slow the wrist and lift the chasen so only the tine tips skim the top. Drag the chasen across the surface in one slow circle to pop any remaining big bubbles, then lift it straight up out of the center.