Well, as of yet there's no way to use a facility other than collect income from it or produce in it. Let's say you have an office,tavern,hotel or casino these are income producing facilities, which basically exist to make you money. On the other hand factories, bactarefinement centers and mines serve to help you produce something.
But did you tell how to actual use a facility?
First we need to know if the facility is owned by yourself or if you are visiting a facility or if you were assigned a facility and of course what type would be useful as well.
ok, in facilities that make income, managers get the income (operators don't and neither do owners, unless they are also manager). Managers can also modify various things like the open status, assign operators etc. For production/mining facilities depending on who owns it, the manager/operator needs to be a specific faction/person.
Operator earns nothing for operating a facility, unless the owner wants to give them something.
Open to all means anyone can enter the facility, and is required for a facility to make income. Open to crewlist means nobody can enter the facility except those people/factions that you put on the crewlist of the facility.
Debt is caused when an income making facility is on a planet with bad stats that causes it to loose money rather than make it. You have to manually pay it off. I am unsure if you have to pay it off to allow it to make positive income once the planets stats are fixed - though at a guess you would have to.