There are several reasons we don’t recommend starting apple trees from seed. 1) Seedling trees grow much larger than commercially available trees and are therefore difficult to manage (more difficult to prune, spray, and harvest). 2) The apple fruit the trees will produce will be nothing like the apple you harvested the seeds from. This is due to the fact that apples are cross-pollinated and highly heterozygous. Cross-pollinated means that bees transfer pollen from one kind of apple tree to another. Therefore an apple seed will inherit two unique sets of genes, one from the tree that the apple grew on and one from the tree that the bee brought pollen from. The fact that apples are highly heterozygous means that each of the seeds in an apple contains genetic information for a tree that is completely different from its parents and siblings, just like we don’t look exactly like either of our parents or siblings. 3) Because of #2 the trees produced may or may not be susceptible to diseases like cedar-apple rust and apple scab, two very common diseases in Nebraska. When you purchase apple trees from a nursery you can choose an apple variety and rootstock that have resistance to these diseases, reducing the amount of fungicide you will need to spray to keep the trees healthy and the fruit edible.
The bottom line is that if you want to grow a certain kind of apple, like Gala or Honeycrisp, you need to buy that variety grafted onto a semi-dwarf rootstock, ideally with resistance to cedar-apple rust and apple scab.
If you have other reasons for wanting to start apple trees from seed, check out Growing New Fruit Tree Plants From Seed from Penn State University. It gives chilling temperatures and durations and describes how to handle young plants.