Summarize:

Purchase several ripe apples, then eat them or cut them until you reach their cores. Carefully remove the seeds from around the cores of the apples, being sure to pick out every seed before disposing of the cores.  Be aware that most apple trees grown by farmers and gardeners come from grafted trees, and are not planted directly from the seed. Planting trees from apple seeds produced highly variable fruit, since apple trees are not guaranteed to grow according to their type or variety. The more seeds you plant, the more likely it will be that one of the trees will produce edible apples, as opposed to less edible varieties like crab apples. There is about a one in ten success rates of seeds growing into apple trees that produce fruit good enough to eat. Try to start the process of preparing the seeds during the fall, so that by the beginning of spring, the seeds are ready for planting. After you extract the seeds from the apple or apples, add the seeds to a bowl of water. If they float, throw them away, because they are less likely to grow. Lay the other seeds out on a paper towel and allow them to dry for three to four weeks. Flip the seeds over every two days so that they dry evenly on both sides. After a couple days of drying, purchase some peat moss. Pour a few tablespoons of the peat moss on the paper towel, then sprinkle on a few drops of water. Use your hands to mix up the peat moss and seeds. After you mix up the seeds and peat moss, pour the mixture into a ziplock bag. Write the date on the bag with a marker, then place the bag in the refrigerator for three months.  The process of storing the seeds in moist, cold conditions is called stratification. Stratification softens the hard outer coat of the seed and encourages the embryo inside the seed to start germinating. After three months, remove them from the refrigerator, and allow them to warm up so that you can plant them.
Remove apple seeds from the cores of several apples. Dry the seeds on a paper towel. Mix the seeds with peat moss. Put the seeds and peat moss in a bag and refrigerate.