The value is determined by the prices that the coin sells at on whatever exchanges that it sells on. I don't think there is any coin whose value is fixed to another currency.

As for what factors affect the value of a coin, the answer depends on the coin. For example, the value of Quark was supported by exposure (pumping, perhaps) by Max Keiser and Bill Still. The value of Dogecoin is a result of the humor associated with the meme.