"Points of sail" refers to the direction in which the boat is sailing in relation to the wind. Close-hauled is sailing as close to the wind as possible, a beam reach with the wind straight from the side, a run dead down wind, etc.
The centerboard is most needed when close-hauled and is not needed at all when running. At points in between, the board is needed in varying degrees, like this in general:
- Close-hauled: board fully down
- Beam reach: board halfway to three-quarters down
- Broad reach: board one-quarter down
- Run: board fully raised
When learning to position the board most effectively, beginners can mark the control line (or top of centerboard trunk if the board's top edge is visible) with a Sharpie or pieces of tape to indicate the different board heights - in order to quickly position the board at different points of sail.
Solo sailors generally lower the board completely before heading up toward the wind, to concentrate on steering and managing the sails. When turning off the wind, leave the board down until the new course is reached and the sails trimmed, and then position the board appropriately. When sailing as a twosome, the crew not at the helm handles the centerboard and sails and can fluidly raise and lower the centerboard in gradual steps through a turn.
A final use of the centerboard is to help right a small sailboat following a capsize. The sailor stands on the centerboard while holding the boat's rail and leaning back, and thereby levers the boat back upright as described here.