What are the effects of crosswind on takeoff?
The upwind aileron is held down in order to keep the crosswind from pushing the airplane downwind. This is called crosswind drift. Usually the aileron begins fully deflected and reduced as it becomes more effective with increased airspeed. Upwind elevator is coupled with downwind rudder, which keeps the airplane in the centerline.

When I have taken off in a glider with a very strong crosswind, I have started the roll all the way on the downwind side of the runway and taken off diagonally upwind in order to  to reduce the crosswind component.