Most apples are grown from grafted trees and will not come true from seed. The seeds might germinate, and they could develop into productive trees, but the fruit might not be similar to the fruit you purchased. Fruit breeders plant thousands of apple seeds every year from controlled crosses they make. Of these seedlings, no more than one or two are expected to make it into commercial production.
If you want an apple tree that develops tasty fruit, you should buy a known variety from a nursery or mail-order source. You can find almost any variety of tree available, and trees you purchase will fruit in a much shorter time. A seed-started tree could take 8-10 years to fruit. Also, apple trees started from seed will have no dwarfing characteristics. Unless you have a large yard, they may be too big for your site.
If you're the adventurous type and would like to start the seeds despite this discouragement, here's how to do it: Remove the seeds from the ripe fruit. Plant them an inch deep in a pot containing potting soil or seed germinating mix. Moisten the soil. Bury the pot outdoors in the ground in fall, or place it in a plastic bag in the refrigerator, away from ripening fruits and vegetables.
Periodically check the soil mix to make certain it stays moist but not wet. After 3-4 months of temperatures just above freezing, move the pot to a location at room temperature (or wait for warm temperatures to develop naturally outdoors). If properly chilled, the seeds should germinate in several weeks.