Growing apple trees from seeds can be both fun and educational. But be aware that the tree you plant probably won't look anything like the parent. Apples that you buy at the store come from hybrid apple trees that are grown by grafting them onto dwarfing rootstock. This keeps the trees small and allows commercial growers to control the type of fruit produced. So you may end up with a very large tree that produces apples that look a lot different than the ones from which you took the seeds.
Remove the seeds from several store-bought apples. Many of the seeds won't germinate so it's best to start with at least 10. Place the seeds on a damp paper towel and fold it several times to make sure the seeds will stay moist. Put the paper towel in a plastic bag and seal it. Leave the bag in your refrigerator for about six weeks.
Prepare small planting containers by filling them with sterile potting mix and adding a little water to moisten the soil. Be sure the containers have drainage holes in the bottom.
Unwrap the paper towel and remove the seeds that have sprouted. Plant each seed in a container by gently pushing it into the potting mix to a depth of about half an inch. Place the containers in a sunny location such as a window sill and add water as needed to keep the soil moist.
Plant your seedlings outside as soon they have outgrown their containers. Space them about 20 feet apart in a well-drained part of your yard. You may have to be patient waiting for your trees to produce apples. It can take five or six years before young apple trees bear any fruit.