Well, according to what you wrote your in a facility, you must walk around until you find a room with a box with what looks like crosshairs in it. As soon as you get to that room, you will see an exit button under travel. Under the travel keys also is a room legend, most useful if you don't know what each room is.
I believe its been set so that players spawn in the entrance room. So yes, when you can see the room map under the buttons that go across the middle of the screen, there should be a button on the left that says [Exit]. Click that and the confirmation afterwards and you will be outside.
I just started on corellia not realizing that I should've waited to pick starting point after jioning faction. Now I'm stuck in the civil center hanger and can't leave to get to the city. There is an air speeder in the hanger, But the Name on it is Koro-2 airspeeder that is not my name it is Kuro. Can you help me please to get out of this building
To further expand, Koro-2 is the name of the type of speeder, like a Victory stardestroyer.
In anycase, you need to go from room to room in the building until you get to the Entrance Room - this should of been the room you started in. Then there should appear an [Exit] Button to the left of the room map. Clicking this, and the confirmation button will put you outside and in the city. Welcome.