How can I buy an unlocked iPhone 5s in the US? My parents are on holiday in the US now, and they were supposed to buy me an iPhone 5s to use in Norway. But they were told in the store that they couldn't buy an unlocked iPhone 5s.

Is this true or have they misunderstood? iPhone 5s is beeing sold unlocked in Norway, so I just couldn't understand why not in the US?
It is up to Apple to decide when and where unlocked iPhones are sold. Currently in the U.S., Apple does not explicitly state that it sells unlocked iPhone 5s - the Apple online store page for iPhone 5s does not mention unlocked phones, unlike the Apple online store in say, Canada.

However, buying directly from Apple and choosing T-Mobile as the carrier means paying the full price, and it may be unlocked (do not purchase from T-Mobile). See this thread titled  iPhone 5s purchased from Apple is not unlocked on the T-Mobile forums for more information. After buying the T-Mobile option from Apple, if it seems locked, activate it with T-Mobile and request T-Mobile for an unlock.

Also note that all unlocked iPhone 5s models sold on Amazon and elsewhere are probably from other countries since the pricing is a lot higher (which may be an indication that it's not easy to get unlocked iPhone 5s in the U.S.).