Remove wiper arms. Open doors, remove bolts that hold the bottom of the a-pillars. Open hood, remove the hood-to-cowl rubber seal. In the valley where the seal was removed, you will see a few of those plastic push screw things (the same kind used to hold the radiator cover on). Take those out. Now you can pop the cowl off. It is only held in place by clips at this point. Work your fingers under the top of the cowl where it meets the windshield and gently pull upwards to disengage the clips. Be very careful as the hard plastic on the 99-04 cowls is pretty easy to break. Installing a new one should be easy but uninstalling them can be tricky if you're trying not to break it. Once you have it loose, you can detach the plastic tubes going to the washer nozzles.
carving corners like a boss