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.
A lot of good points here. I think the fall in price of the primary crypto currency- bitcoin definitely works as a powerful factor increasing prices of other alternate currencies like litecoin.