The problem with Lonnie's answer is that apples are notorious for not breeding true to type. And apple trees are exceptionally difficult to grow from mere cuttings. If you want to ensure the same variety of apple, it's best done by grafting onto an existing tree or root, or by 'rootstocking'. The latter involves producing new roots, by either pegging a branch to the ground, or using the trunk, and piling e.g., damp sawdust around it. New roots form and then, only when the tree is fully dormant in winter, they're cut off and planted on.