Here's a beginner's guide to plant propagation

Learning to propagate plants—to make new plants from existing ones in your home and garden—is one of the most exciting and rewarding aspects of gardening. Many of the methods are easy, and you don’t need fancy or expensive tools. Propagation is cheaper than buying large numbers of plants, so with a little time and effort you can fill your garden quickly at minimal cost. Propagating new plants will keep your house and garden full of vigorous specimens, and you’ll probably have plenty to give away, too!
You can reproduce most plants by several methods. There are two major types of propagation: sexual and asexual. Sexual propagation involves seeds, which are produced by the fusion of male and female reproductive cells. Asexual propagation methods use the vegetative parts of a plant: roots, stems, buds, and leaves. Division, cuttings, layering, budding, and grafting are all asexual methods. Spores (produced by ferns and mosses) may look like seeds, but they are technically asexual structures, because they have a specialized way of forming new plants. 
Select a technique by considering the plant you are working with, the materials you have, the season, and the amount of time you are willing to wait for a new plant.
Growing from seed is an inexpensive way to produce large numbers of plants. Annuals, biennials, and vegetables are almost always reproduced by seed. You can also grow perennials, shrubs, and trees from seed, although the seedlings they produce may not resemble the parent plants. Raising seeds requires few materials: a container, a growing medium, and seeds. The time to sow seeds depends on the type of plant. For most garden plants, you can sow seeds indoors in late winter or outdoors in spring. Tree, shrub, and many perennial seeds may need a cold period or other treatment before they will germinate. Depending on the type of plant, it could take anywhere from weeks to years to get a garden-sized specimen. For complete information on growing plants from seeds, see the Seed Starting and Seed Saving entry. 
Spores are the reproductive structures of ferns and mosses. To produce new plants, sow these dustlike “seeds” on a sterile medium and cover them to maintain humidity and prevent contamination. Clear plastic shoe boxes or cups are ideal containers for propagation. You can collect spores from your own ferns or buy them from specialty catalogs. You can sow spores whenever they are available. The new plants will be ready for the garden after a period of months or years. 
Division is an easy way to produce more plants with almost 100 percent success. This method involves digging up an established plant and separating it into several pieces. Division is used for bulbs and mat-, clump-, or crown-forming plants, including ferns, bamboos, bugleweed, daylilies, and hostas. Single-stemmed plants like trees cannot be divided. 
All you’ll need for division is a tool to dig up the plant, and your hands or a sharp implement to separate the pieces. You can divide most plants in either spring or fall. Division produces full-sized plants that can be placed directly in the garden. 
Cuttings are pieces of leaves, stems, and/or roots that are separated from a parent plant. When placed in the proper conditions, these pieces form new roots and shoots. Stem cuttings are used for a wide range of plants, including geraniums, pachysandra, and coleus. Use root cuttings for perennials such as Oriental poppies (Papaver orientale) or globe thistles (Echinops spp.) and some trees, including goldenrain tree (Koelreuteria paniculata). You can also try leaf petiole cuttings, used for African violets and peperomias, and leaf pieces, used for such plants as gloxinias and snake plant (Sansevieria spp.). 
The materials you’ll need depend on the plant and the method you are using. Leaf petiole cuttings of African violets will root in a simple glass of water. You can stick stem and root cuttings in a pot or flat of regular potting soil. A plastic bag or other clear cover will help to maintain high humidity around the cuttings. More complicated structures, such as cold frames and mist boxes, are good for hard-to-root shrub and tree cuttings. Plants reproduced by cuttings can be ready for the garden in a matter of weeks or months.