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There are basically two ways of obtaining a bonsai- either you buy it or you grow it. If you buy one you lose some of the absorbing work of pruning it and determining its shape, but you do see a mature end result.
You can buy one fully grown, container and all, from a specialist nursery. Or- from autumn to spring when they are resting- you can buy one grown but 'root-wrapped' (that is, with its ball of soil protectively wrapped in some way) rather than in a container. You then plant it yourself, which means you have the choice of container.
Alternatively, as bonsai are usually rather expensive to buy, you could grow your own from a seed, seedling or cutting. Oak, Willow, Beech, Sycamore, and Conifers are easy to grow in this way if you give them enough warmth, moisture and air.
The drawback here is that it can take up to 100 years to develop a mature bonsai!
The major points to look for when buying or growing a bonsai are that the plant is small and attractive, that the trunk is thick in proportion to the height, that the plant itself and its roots look healthy, and that it has small leaves.
An Acorn or Chestnut will grow if you plant it. You can take a cutting from a tree. Or, if you are lucky, you may find a suitable seedling. Cuttings should be 3 inches long, cut just below a leaf node so that they can drink easily. Take soft
wood cuttings in the spring, and hard wood ones in autumn choosing wood of that year's growth.
To plant, make holes in the side and bottom of a pot (if it is clay you will need to drill these, if plastic you can make them using a sharp knife). Put crocks and gravel at the bottom of the pot to help drainage, then fill the pot with a sandy compost. A seed should be planted about its own height below the soil, a cutting about one third of its length, and a seedling as a plant. Leave half an inch at the top of the pot for watering.
As roots come through the holes in the pot snip them off, and after one year in the pot if it is a cutting or seedling, or two or three years for a seed, repot into its new container and, later, start pruning the top growth very carefully.