Willows are easy to propagate and we get a question like yours often, Below is a response on the IA State website that I think answers your question well. 

Question:

How can I propagate a willow?

Answer:

Willows (Salix species) are easily propagated by hardwood cuttings. On a mild winter day in late February or early March (temperatures should be above freezing), go out and collect cutting material. Prune off branches that are about ½ inch in diameter. Bring the branches indoors and cut the branches into 12 to 18 inch sections. Bundle the 12- to 18-inch-long cuttings together with string or twine. Place the bundled cuttings in a plastic bag that contains some lightly moistened peat moss. Place the plastic bag in the refrigerator. In early April, remove the cuttings from the refrigerator and stick the cuttings into the ground. Place the bottom 6 to 8 inches of the cuttings in the soil. Willow cuttings root quite easily. The cuttings should begin to root and leaf out within a few weeks. An alternate rooting method is to place the cuttings in a container of water indoors. Regularly change the water. When the cuttings have developed good root systems, remove them from the water and plant outdoors.

More details about taking hardwood cuttings can be found in this article: Propagation of Trees, Shrubs, and Vines, from Hardwood Cuttings.