Question:  How can I find the heat of fusion of ice in Joules per gram?

Answer:

To find the heat of fusion of ice in Joules per gram, measure the amount of energy (in Joules) it takes to melt a known quantity of ice.  Divide this amount of energy by the number of grams of ice melted to get your answer.

Experimentally, the way this is done is through a process called calorimetry.  Calorimetry requires a device called a calorimeter, which involves making some chemical or physical process take place in a small area surrounded by a measurable quantity of water.  Because the temperature increase in the water is directly caused by the energy absorbed or given off by the process taking place, you can easily determine the heat change caused by the process.