What is the value of a 2001 United States gold liberty coin?

You need to know its weight. US gold bullion coins have their weight in ounces on the back, along with an artificial denomination.

In general these retail slightly above the current price of gold. For example, if you have a 1/10 oz coin and the cost of gold is $1050 per ounce, it would have $105 worth of gold in it, and might retail for 5% or so above that amount.