How does one know the rarity of a Yu-Gi-Oh card?

Good question! But the rarity means Absolutely nothing if the card isn't in mint or near-mint condition. With that said, there are several "levels" of rarity in Yu-Gi-Oh! cards. The rarest are Secret rare, I believe. They have a sparkly holographic picture and a sparkly silver foil name. Sorry if I'm no help. I can't afford the cards anymore. But my best advice for you is buy a price guide or Beckett magazine and look them up.