When you want to propagate a weeping willow branch, the first thing you need to do is find a good, healthy branch that is at least 18 inches long. Once you have found a good branch, cut it off of the tree at a 45-degree angle about six inches from the end of the branch. Next, you will need to strip all of the leaves off of the branch except for the topmost leaves. Once you have done this, dip the end of the branch in rooting hormone and then plant it in a pot filled with moistened potting soil. Place the pot in an area that receives indirect sunlight and keep the soil moist but not soggy. In four to six weeks, roots should begin to form and after three months you can transplant your new weeping willow into your garden.