Here's a beginner's guide to plant propagation

Plant propogation is fun and exciting.Layering
Layering is a way to get stems to root while they are still attached to the parent plant. Some plants produce layers naturally. Strawberries form rooted plantlets on runners; raspberries produce new plants where the stem tips touch the ground. The technique of simple layering involves bending a low-growing stem to ground level and burying a few inches of the stem behind the tip. Simple layering is an easy way to reproduce such plants as camellias, forsythias, and magnolias. To air layer, you shallowly wound a stem a few inches below the tip to stimulate root production, and then wrap moist sphagnum moss around the stem. Covering the moss with a thin sheet of plastic holds in moisture and secures the moss to the stem. Weeping fig trees (Ficus benjamina), corn plants (Dracaena fragrans), and witch hazels (Hamamelis spp.) are all good candidates for air layering. 
You don’t need much equipment to try these techniques. A trowel (for digging the trench) is sufficient for simple layering. For air layering, you’ll need sphagnum moss, waterproof tape, a piece of thin plastic, and a knife. Early spring is the best time for simple layering. For outdoor plants, you can set up air layers in spring or late summer. Indoor air layers can be started anytime. It will probably take several months to a year to get a new well-rooted plant. For more information, see the Layering entry.
Grafting is a more advanced propagation technique. It involves joining a stem piece of one plant (the scion) to the root system of another plant (the rootstock) in such a way that the parts unite and continue to grow. You can reproduce many types of trees by grafting, including pines (Pinus spp.) and rhododendrons, and even some herbaceous plants, such as cacti. Grafting has several advantages over other propagation methods. It allows you to propagate plants that are difficult to raise from seeds or cuttings. Through grafting, you can produce a plant adapted to your particular needs. Some rootstocks have a dwarfing effect, while others encourage vigorous top growth. They can also provide tolerance to soilborne insects and diseases, or to less-than-perfect soil conditions
The most important grafting tool is a sharp knife. You may also need string or tape (to keep the graft pieces together) and grafting wax (to prevent water loss and avoid contamination). You’ll have to have suitable rootstocks, too. You can raise your own from seeds or cuttings, or buy them from a specialty catalog or nursery. Spring is the most common time for grafting. Herbaceous plants will join successfully in a few weeks; woody plant grafts usually take a month or two to unite firmly and begin growing. See the Grafting entry for more details on this technique.
Budding is a particular type of grafting. In this method, you use only a single bud from the desired plant. Budding is commonly used to propagate fruit trees as well as ornamentals, such as hybrid tea roses. For the home gardener, the advantages of budding are similar to those of grafting. In some cases, budding is more successful than grafting because it is easier to get close contact between the bud and the rootstock. Budding also allows you to propagate more plants if you have a limited amount of scion material. 
For this technique, you’ll need a sharp knife and some string or tape to secure the bud to the stem. As with grafting, compatible rootstock plants are necessary. Budding is best done in late summer or early fall. Buds inserted at this time will produce new growth the following spring.