Even with a brisk crosswind blowing across the runway, many pilots are reluctant (or neglect) to use all of the available flight controls during crosswind takeoffs and landings.
As the FAA Airplane Flying Handbook explains:
The technique used during the initial takeoff roll in a crosswind is generally the same as the technique used in a normal takeoff roll, except that the pilot must apply aileron pressure into the crosswind. This raises the aileron on the upwind wing, imposing a downward force on the wing to counteract the lifting force of the crosswind; and thus preventing the wing from rising…
While taxiing into takeoff position, it is essential that the pilot check the windsock and other wind direction indicators for the presence of a crosswind. If a crosswind is present, the pilot should apply full aileron pressure into the wind while beginning the takeoff roll. The pilot should maintain this control position, as the airplane accelerates, and until the ailerons become effective in maneuvering the airplane about its longitudinal axis. As the ailerons become effective, the pilot will feel an increase in pressure on the aileron control. (6-6)
The goal while landing, as described in the FAA Private Pilot ACS is to:
Touch down at a proper pitch attitude with minimum sink rate, no side drift, and with the airplane’s longitudinal axis aligned with the center of the runway. (Task IV. Takeoffs, Landings, and Go-Arounds)
When landing with a crosswind, you must also apply and hold aileron inputs into the wind while using rudder and elevator pressures to track the centerline, keep the aircraft aligned with the runway, and touch down in the proper pitch attitude.