You have 2 options: Replace the entire assembly, wich includes teh fuel level sending unit, pump...but i don know if the pressure regulator is included. May cost up to 280 $. Only the pump, about 70, but is hard to replace it...I did it that way. It was a headhache. If you are keeping a stock engine, i would recommend to spend the 200+ bucks to buy the entire assembly. Remember to use a new fuel filter!
Start by blocking the front wheels then lift the car and support it securely on a jack stand. Remove the rear wheel. At this time, you may want to clean the underside of the car with a household pressure washer because these cars are getting old and very dirty, at least here in Mexicali.

Next step, get under the car and remove the thing that looks like a fuel filter (Its secured by a 10mm bolt) and unplug the electrical connector. Remember to first move the Red tab, the unplug it. (Be careful with that canister, its full of gasoline)

Now, the Factory Service Manual for 97 and 99 Neons, says there's a hole to drain the tank, but my car didn't have, so I removed the filler tube to drain the tank by Siphoning it. DO NOT DO IT USING YOUR MOUTH. To remove the tube, remove the filler cap and the screws. The filler tube uses a 1/4" clamp. Dont forget the Ground Strap (10mm screw) and the vapor lines. I used a very small hose to siphon the fuel. The tank is about 13 gallons, so get a fuel safe container with a sufficient capacity.

Support tank with a jack. Loosen
tank mounting straps (13mm) and lower tank slowly. Before removing the 13mm bolts, soak them with penetrating oil,

The fuel tank is now out of the car, before attempting to remove the fuel pump, thoroughly wash the area of the pump.

There's a special wrench to remove the big nut that holds the fuel pump assembly. I used just a screw driver and a heavy 1/2" drive ratchet to remove the lock nut. Check out the mark, in the pic is green, when tightening the nut, be careful to not over-tight it. The manual specifies 40.5 ft-lb Torque.

There's a alignment tab on the fuel pump assembly. I dindt find a new O-ring, I used the old one. It was very hard to put the assy. on the tank, so i lubed the o ring with some fabric softener.

Installation is the Reverse of Removal.