There should be NO drips from the radiator drain petcock. Keep an eye on this, because if you lose too much coolant you can damage the engine. The steam might just be from spilled coolant. It should stop soon. If you continue to see steam you have a problem that needs attention.
I hope you’ve learned by now that you must check the coolant level in the radiator itself. The overflow bottle can look OK even if the radiator is low. This is usually a sign of a bad radiator cap.
Keep the radiator full. You cannot add too much. The radiator should be completely full at all times, right up to the bottom of the cap.
If the radiator is leaking, take the car to a radiator specialist. You can find one in your local phone book. You’ll save money in the long run letting a specialist deal with cooling system issues.
Don’t give up on this car. We had a '91 Corolla in my family that was still running strong when we sold it two years ago with 175,000 miles on the odometer. The buyer still uses it as daily transportation.