Plant propagation is the process of creating new plants from a variety of sources: seeds, cuttings, bulbs and other plant parts. Plant propagation can also refer to the artificial or natural dispersal of plants.

Sexual Reproduction – pollination (plants or trees that have flowers)
Asexual Reproduction *Natural
*Artificial

Natural Methods of Asexual Reproduction
Natural methods of asexual reproduction include strategies that plants have developed to self-propagate. Many plants, such as ginger, onion, gladioli, and dahlia, continue to grow from buds that are present on the surface of the stem. In some plants, such as the sweet potato, adventitious roots or runners (stolons) can give rise to new plants . In Bryophyllum and kalanchoe, the leaves have small buds on their margins. When these are detached from the plant, they grow into independent plants; they may also start growing into independent plants if the leaf touches the soil. Some plants can be propagated through cuttings alone.

Runners: asexual reproduction
A stolon, or runner, is a stem that runs along the ground. At the nodes, it forms adventitious roots and buds that grow into a new plant.

Artificial Methods of Asexual Reproduction
Artificial methods of asexual reproduction are frequently employed to give rise to new, and sometimes novel, plants. They include grafting, cutting, layering, and micropropagation.
Grafting
Grafting has long been used to produce novel varieties of roses, citrus species, and other plants. In grafting, two plant species are used: part of the stem of the desirable plant is grafted onto a rooted plant called the stock. The part that is grafted or attached is called the scion . Both are cut at an oblique angle (any angle other than a right angle), placed in close contact with each other, and are then held together. Matching up these two surfaces as closely as possible is extremely important because these will be holding the plant together. The vascular systems of the two plants grow and fuse, forming a graft. After a period of time, the scion starts producing shoots, eventually bearing flowers and fruits. Grafting is widely used in viticulture (grape growing) and the citrus industry. Scions capable of producing a particular fruit variety are grafted onto root stock with specific resistance to disease.

Grafting
Grafting is an artificial method of asexual reproduction used to produce plants combining favorable stem characteristics with favorable root characteristics. The stem of the plant to be grafted is known as the scion, and the root is called the stock.

Cutting
Plants such as coleus and money plant are propagated through stem cuttings where a portion of the stem containing nodes and internodes is placed in moist soil and allowed to root. In some species, stems can start producing a root even when placed only in water. For example, leaves of the African violet will root if kept undisturbed in water for several weeks.
Layering
Layering is a method in which a stem attached to the plant is bent and covered with soil . Young stems that can be bent easily without any injury are the preferred plant for this method. Jasmine and bougainvillea (paper flower) can be propagated this way. In some plants, a modified form of layering known as air layering is employed. A portion of the bark or outermost covering of the stem is removed and covered with moss, which is then taped. Some gardeners also apply rooting hormone. After some time, roots will appear; this portion of the plant can be removed and transplanted into a separate pot.

Layering
In layering, a part of the stem is buried so that it forms a new plant.

Micropropagation
Micropropagation (also called plant tissue culture) is a method of propagating a large number of plants from a single plant in a short time under laboratory conditions . This method allows propagation of rare, endangered species that may be difficult to grow under natural conditions, are economically important, or are in demand as disease-free plants.
To start plant tissue culture, a part of the plant such as a stem, leaf, embryo, anther, or seed can be used. The plant material is thoroughly sterilized using a combination of chemical treatments standardized for that species. Under sterile conditions, the plant material is placed on a plant tissue culture medium that contains all the minerals, vitamins, and hormones required by the plant. The plant part often gives rise to an undifferentiated mass, known as a callus, from which, after a period of time, individual plantlets begin to grow. These can be separated; they are first grown under greenhouse conditions before they are moved to field conditions.

Source: Boundless. “Natural and Artificial Methods of Asexual Reproduction in Plants.” Boundless Biology. Boundless, 08 Jan. 2016. Retrieved 16 Apr. 2016 from https://www.boundless.com/biology/textbooks/boundless-biology-textbook/plant-reproduction-32/asexual-reproduction-191/natural-and-artificial-methods-of-asexual-reproduction-in-plants-729-11958/

Marcotting is a form of vegetative reproduction that consists in inducing rooting of part of a tree branch. After rooting is induced, the branch is cut and put in a nursery to develop buds and become an independent plant.

Grafting is a form of plant propagation that consists of joining two separate plant parts together to create a new plant. The two parts to a graft include the scion, or the top branch, and the understock, also called the rootstock, which is the bottom portion with the roots.
Compatibility
While grafting can create interesting and appealing colors and shapes, grafting is not universally compatible among different plant species. Only closely related plants can be grafted together, but most plants of the same genus and species can usually be grafted regardless of variety. Generally, plants that share the same genus but are a different species will not create a perfect union between the scion and stock. Plants from differing families will not graft at all. When selecting plants for wedge grafting, ensure compatibility so that you do not accidentally damage or kill the host plant.
Selecting a Scion
Scions are the branches of healthy plants that will be grafted onto the host stock. It's important to select scions that are only from healthy, thriving plants that show no signs of disease. Grafting a diseased scion may result in the disease being transmitted to the host plant. You do not need to purchase special equipment for a successful wedge graft, but it is important that whatever knife or pruning sheers you use to cut your scion are very sharp. A smooth, clean cut is needed for best results.
Cutting the Scion
Cut two scion limbs near the stock at a 45-degree angle from both sides. It's OK to use a knife or pruning sheers to make the cuts, but make sure that the cuts are straight and do not contain jagged edges. The goal is to create two pointed, tapered wedges that will fit into a horizontal cut on the host stock. The base of each scion should measure about 1/4 inch in diameter and be about 6 inches long with at least three buds per scion.
Grafting the Scion
Physically connect the scion with the host stock. The stock should be cut horizontally and cleanly. Use a long, sharp knife to make a wedge-shaped cut down the center of the stock, leaving about a 1-inch V-shaped cut in the wood. Insert a clefting tool and gently pull back to separate the wedge. Place the pointed tip of each scion into the horizontal incision. Align each scion so that the bark of the scion matches the bark of the host stock. This will align the cambium of each scion, which is critical to a successful graft. Pour grafting wax or grafting paint over the entire exposed area of the graft. After about three months of growth, remove the scion that appears to have grown the least. This will give the most successful scion the best