If the reservoir is empty you can just add coolant, but also allow the engine to run and check for any coolant leaks.
Coolant should not normally need refilled unless you have a leak such as a bad water bump, bad radiator hose, heater hose, or even a bad headgasket.
When water pumps go bad they leak out the weep hole and it's a sign you need a new water pump.
But not all coolant leaks are from the water pump and so if you're losing coolant you should look around the vehicle for leaks and fix the coolant leak as soon as possible.
It's OK to mix coolants as long as the coolants are the same coolants and compatible with each other.
Different brands of coolants can be mixed, but the coolants need to be the same to avoid any problems such as gelling, clogging, corrosion, overheating etc.
You can add new coolant to old coolant as long as the coolants are compatible and the same.
If you just need to top off coolant it's okay to add some new coolant in with the old coolant as long as the old coolant is still good and not contaminated.
Make sure you use the correct coolant as mixing different types of coolants could cause issues with the cooling system and even lead to corrosion and clogging or even gelling.
It's best to drain out the old coolant and put in fresh new coolant, but if the coolant level is down just a little bit then adding a bit of new coolant to the old coolant is not usually a problem.
When adding coolant start the engine with the radiator cap off or if your vehicle uses a coolant reservoir you can add the coolant to the reservoir and allow the engine to idle for a few minutes.
Watch the temperature gauge and ensure that it does not overheat.
The engine temperature may go up and then drop back down when the thermostat opens up.
If you have an owners manual for your vehicle the coolant type should be listed in the owners manual.
Or if not you can input your vehicles make and model and year into Google search and it will show you what type of coolant your specific vehicle takes.