This the recommended procedure for filling the cooling system on the Neon; lifting the front of the car is the key part to force any air out. If the car was on an inclined driveway or street would also work.
Step 1
Allow the car’s engine to cool completely. Chock the car’s rear wheels and set the parking brake. Lift the front of the car with a floor jack and secure it on a set of jack stands. Remove the cap from the coolant overflow tank.
Step 2
Crawl under the car and look toward the bottom-right corner of the radiator. On top of the lower radiator support, hidden behind a length of wiring conduit, is a circular drain plug with a fin sticking out of it. You may have to feel for it.
Step 3
Slide a drain pan under the radiator and turn the drain valve counterclockwise with a pair of pliers. Wait for all of the coolant to drain out and then close the valve.
Step 4
Add coolant to the radiator through the coolant overflow tank; the radiator on this car doesn’t have a built-in cap, so the only way to add coolant to it is through the overflow tank. It should take about 6.5 quarts of coolant mix, including one quart in the overflow tank itself. Leave the coolant tank cap off.
Step 5
Start the engine and monitor the overflow tank. Dodge designed the car so that the fitting for the overflow tank tube and the expansion tank are the highest points in the cooling system. Air trapped in the cooling system will naturally rise out of the tank.
Step 6
Top up the coolant tank as necessary as the engine idles up to operating temperature, and install the cap. When the engine reaches operating temperature, shut the engine down. As the engine cools, it will create a vacuum in the cooling system that will draw any needed coolant in through the expansion tank.
Step 7
Start the engine and allow it to idle again until it reaches operating temperature. Add coolant to the expansion tank until it reaches the “Hot” line on the tank.