Protect the floor beneath the leak with a drop cloth. Remove furniture if necessary.
Remove any loose ceiling texture by scraping it with a putty knife. Use a ladder to help you reach the ceiling.
Replace the ceiling texture by spraying area with ceiling texture patch material. It comes in an aerosol can with a tip like on a whipped cream can, which allows you to spray it straight up on the ceiling. Allow to dry thoroughly.
Paint the newly textured area. If it is small, use a soft brush dipped in paint and use a dabbing motion to avoid removing texture as you paint. If the area is large, use a long napped roller with an extension arm.
Clean the painting tools, remove the drop cloth and refurnish the room.