This is a regular verb. It follows the conjugation pattern of the verb hablar.
PresentPresente
Su sonrisa conquista a todo el mundo.
Her smile wins everyone over.
PreteritePretérito indefinido
Los romanos conquistaron gran parte de Europa.
The Romans conquered a large part of Europe.
FutureFuturo
Con ese postre conquistarás a mis padres.
With that dessert you will win over my parents.