In the plastic jug on the left firwall be sure to fill it to the "COLD" line if the engine is cold which it should be or you would not have opened the cap.
Drain the radiator on the 1988 Cavalier. Take of the water pump belt. If the fan and shroud are in the way then remove them. unbolt and remove the pump. Bolt up the new pump and put the belt back on. Put the shroud and fan on if they were removed. Fill the radiator back up.
A 1999 Cavalier does not use Freon as a refrigerant.
You don't put water in your radiator, you put antifreeze.
You should always use a 50/50 mix of antifreeze and water.
**I meant to add that the radiator cap is not to be found on this vehicle. Can it go into the coolant fill tank?
No. Let it cool down before you open the radiator cap and then put water in the radiator
You can put anti-freeze into the search tank of your Chevy Cavalier. Newer Chevy Cavaliers have a sealed radiator and the search tank is the only place you can put anti-freeze into the system.
An easy way to flush a radiator is to remove the bottom hose from the radiator, and put a garden hose in the top fill hole, turn the water on, on the garden hose and let the water push the water out of the radiator. Do not start the truck. This is for flushing a radiator, not an engine. Dont forget to reattatch the bottom hose and refill the radiator as water will also flow out of the engine and will now be low.
Water
When a car is hot, keep the car running and add water to the radiator. When a car is cold, you can simply put the water into the radiator.
To replace the Cavaliers water pump, drain the radiator. Remove the pumps drive belt. Unbolt the pump and take it off ( you might have to take the fan and shroud off to get to the pump.) Install the new pump and put the belt back on. Refill the radiator with antifreeze.
You can put ice in your radiator. Keep in mind that the ice is just water and you should have SAE certified anti-freeze in your radiator