If by "my airport" you mean the place where you started, then that is already a base/focus city. No need (and not possible) to create it again.
Otherwise, in the Gates menu look for the "Create Base" base option. If you select it there should appear a dropdown listbox listing airports where you can create a new base. Just select it and click the appropiate button.
Oh, BTW, creating a base costs 60x the monthly rent for one gate at that airport. Make sure you have enough money available.
