Two major problems face the gardener who has decided to try growing an apple tree indoors. The first is the physical space required. A full-grown apple tree can easily reach 20 feet in height and diameter. Unless you have a very large indoor space, you will want to grow a dwarf variety. The second problem is lack of pollination, but if you just want the apple tree for aesthetic reasons---and not the fruit---this won't be a problem.
Purchase a dwarf apple tree sapling from a reputable nursery. Because dwarf apple trees are grafted as opposed to being bred, it is necessary to buy them already partially grown. Most nurseries will not sell these grafted dwarf trees until they are roughly a year old.
Transplant the sapling into a tree-size planter. Make sure not to cut or damage the roots in the process. Fill in with potting soil.
Attach the trunk to growth guide stakes. These stakes will not only offer support for your dwarf apple tree sapling, they will also encourage growth in a direction of your choosing.
Test the pH level of the soil with a standard soil testing kit. Dwarf apple trees grow best in soil with a pH of around 6.5. The pH of the soil can be raised by adding lime to the mixture. To lower the pH level, try adding a sulfurous material such as gypsum or cottonseed meal.
Water the tree regularly. Because the indoor tree will not be able to benefit from rainfall or dew condensation, it is up to you to make sure it gets plenty of water. The soil should be kept damp to the touch but not soggy.