How do I get air out of the coolant system?

Okay, normally on that system you fill it with coolant in the radiator and coolant reservoir, then run the engine to get it to operating temperature. Now shut it off and let it cool fully, check the coolant level and add as needed, after about 2 heat cycles it should be purged of any air, and you can then run it and see if the reservoir shows it full when hot and cold. If you have to keep adding coolant once, it's full you might want to get a cooling system pressure tester and see if the system shows any leaks. You can usually find them as loaner tools at many of the chain parts stores.

https://www.2carpros.com/articles/radiator-pressure-test
https://www.2carpros.com/articles/coolant-flush-and-refill-all-cars