Before planting, apple seeds will need a dormancy period, called "after ripening." You can accomplish this through stratification: place the seeds in moist peat moss or sand in a small container and put the container in the back of the refrigerator for three to four months.
After stratification, plant apple seeds in seed trays. Use a mixture of half peat moss and half vermiculite for the potting medium. Water the seeds and enclose them in a large plastic bag or a makeshift plastic tent. Poke a few holes in the plastic to encourage air circulation. Keep the covered trays in a warm, dimly lit room as you wait for the seeds to germinate. Depending upon the apple variety you choose, germination may take up to two months.
Keep germinated seedlings indoors near a south window if you can. You want to provide as much exposure to sunlight as possible. Keep the seedlings indoors for several weeks so they can grow stronger and taller. Water them and fertilize with a houseplant fertilizer according to package directions. Harden off the seedlings before planting outdoors in early fall.
Plant the apple tree seedling in a location that gets full sun. Choose a site with good drainage. Water the young tree well and mulch in a 12-inch radius around the tree to help control weeds and retain moisture. Put down two to three inches of mulch. Water the young tree weekly and pull weeds so they do not compete with the young tree.