Windshield wipers are far more complex than they may appear. A clicking noise that is present denotes a structural failure in the windshield wiper arm. The motor at the base of the windshield wiper arm is rotating, but the arm it is supposed to be attached to has become separated from the motor axle. The clicking is the piece of the arm that is still attached, hitting the inside of the wiper arm every time you activate the wipers.
Turn the car off and place it in park to ensure a stable working platform. Examine the wiper arm for damage; the outer plastic panel may be pristine so you need to pull the arm up. Look at the underside where the structural elements are, then trace from the motor axle outwards to find the break in the arm. If there is no break, then the nut attaching the arm to the axle may be broken.
Pry the arm off the nut assembly with a flathead screwdriver. There will be a pressure clip close to the nut. Press down firmly and shimmy it out. Pull the arm off and pry the nut cap off the nut that anchors the attachment point to the motor axle.
Rotate the nut off of the motor axle until the attachment point comes off. The wrench size that you need will depend on the make and model of the car. Do not use a power tool as there is danger of damage to the plastic parts of the arm. Once the nut is off, the end of the wiper arm will come off as well. There will be broken pieces of metal falling out of the arm as you do so. Use a magnet to pick up the pieces and stop them from clogging vents.
Rotate in a replacement bolt in on the arm end. Replace the cap and then slide the wiper arm back into the end point. Use the flathead screwdriver to exert greater pressure on the arm if you have difficulty slipping it into the pressure clip.