vědět = to know (a fact) (similar to Portuguese 'saber' or German 'wissen' or Dutch 'weten')

znát = to know, to be acquainted/familiar with (similar to Portuguese 'conhecer' or German/Dutch 'kennen')

Znát is followed by an object (or it's in the same sentence). Vědět is followed by a dependent clause or the pronoun to.