If Bitcoins aren't tied to a conventional currency, how did they get so valuable?
Bitcoin is the peoples money. People are giving it a value because they rule it themselves. It is not like traditional government money where government can affect the prices. Hence this causes bitcoin to be up or down, expensive or cheap, whatever the price of bitcoin is actually decided upon what people value it. The value of it comes from the chances of not being tied to governments or corporations and having your own currency that you can call yours without anyone meddling with it.
All things in this world get their value based on demand. This demand is being decided by the supply. This is one of the core concept of every economics which applies to bitcoin ecosystem too. You sound like a school boy, go and educate on this from wiki pages before asking any more doubts from this community.