2004 honda civic lx 4 door?

Depending on the mileage it could be the throw out bearing and to do this yourself you will need to pull the axles and the trans-axle out completely and this is a very complicated job for you to do....

Sound like your axle cv boots are torn open. Park your car and turn your steering wheel to the farthest right. Grab a flashlight and look behind your wheel hub. You should see a ribbed plunger looking rubber along the axle. Look for signs of thick grease around the area and open tears on the rubber boot itself.

If you see these signs, then you need to replace your axle cv boots. These rubber boots hold a lot of grease to lubricate and protect your axle joints. When your axle cv boots tear open, all the grease finds away out exposing your axle joints which eventually will make clicking sounds anytime you engage your clutch.

When you engage your clutch, you provide torque to the axle so it can spin which in turn spins the cv joints making the clicking sounds.

You can visit your local auto parts store and either buy a CV Boot Joint kit to replace the old or buy a whole new axle which comes with pre-installed CV boots for both ends.

Good luck!