This is a regular verb. It follows the conjugation pattern of the verb falar.
Present:
A Ana vigia as crianças no parque.
Ana watches the children at the park.
Preterite:
O Miguel vigiou a entrada a noite toda.
O Miguel vigiou a entrada toda a noite.
Miguel guarded the entrance all night.
Conditional:
A Clara vigiaria a casa enquanto eles viajassem.
Clara would watch the house while they travel.