I am confused on what all is involved in "bleeding" the system. Are there more steps than just emptying all the coolant from the engine and the radiator?
Yes there's a bleed screw used to relieve pressure gradually so air bubbles/pockets aren't in the cooling system.
Here's an excerpt
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Bleeding[/SIZE]
Radiator mounted expansion tank:
1. Loosen the bleed screw
on top of radiator expansion tank and let the coolant flow out as you pour it in the reservoir. Tighten the screw when the flow out is free of air bubbles.
Separate expansion tank:
1. Loosen the bleed screw
on top of thermostat housing and let the coolant flow out as you pour it in the reservoir. Tighten the screw when the flow out is smooth and free of air bubbles.
2. Set the temperature setting to full warm and start engine.
3. When the car is going to reach his normal temperature you might going to need to add more coolant. Always check the coolant level.
4. With engine idling at normal temperature, open the bleed screw and tighten it when coolant is spilling out smoothly and free of air bubbles.
5. Repeat bleeding, and again and again.
6. Do it a few times to avoid overheating.