Everyone likes free plants and cuttings are an excellent way to increase the number and variety of the plants in your garden for just the cost of some rooting hormone. Some plants root easily, some are more difficult, but all are worth the effort. The advantages to starting from cuttings rather than seeds include getting starts identical to the parent plant, faster flowering, and increasing your stock before the parent is old enough to set seed.
Chose a section of the branch from which to take the cutting. This can vary from plant to plant. Softwood cuttings are made at the tip of a branch, several leaf nodes down. Hardwood cuttings are done at the more mature sections of a branch, cut into pieces, with each containing three or four nodes.
Cut about 1/4 inch below a leaf node, the point at which new roots will sprout. Prune the leaves on the cutting in half, perhaps more if they are large, such as hydrangeas.
Dip the cutting in rooting hormone powder (available at most gardening centers) and insert about half an inch into a pot filled with sterile, moist sand. Pack the sand around the cutting. Take at least three cuttings to assure success with at least one of them, though many plants will give you a 100 percent success rate.
Cover the pot with clear plastic. Support the plastic with wooden chopsticks to create an air space around the cutting. The plastic will keep the air around the cuttings moist until they have enough roots to gather water. Make sure the cuttings have as much light as possible without leaving them in direct sunlight, which could burn the leaves and dry out the tiny plants. The light provides the energy for forming new roots.
In a week (more for some plants) gently pull on the cutting. Don't pull so hard that you tear the new roots. When you're sure the roots have grown to 1/2 inch or so in length, you can remove the plastic. A few weeks later you can pot up your new plants.