Refilling the cooling system

I've just replaced my heater core and thermostat and added a reasonable amount of water to the system as a test.

The system doesn't leak anymore but I don't think it's full either.

I saw a sticker under the hood that read for proper operation the system must be full.

Right now it has 100% water in it due to the heater core leak and me refilling the system with water every day for about two weeks (at the end it was a squirter when under pressure).

There's also a plastic reservoir with a small hose from the filling spout on the radiator running to it that says for coolant only. And I think that's important too. At this point the reservoir is empty.

How does the reservoir fit in, and how do I refill the system after replacing the thermostat and leaky heater core?

And since we're on the subject, I've always wanted to know why the cooling system works best under pressure? I used to have a car where, for a few days, I used a foot sock for a radiator cap. It didn't work very well. Well at least I know better than that now.

Help!