Well, I'm foggy in my memory, but apple trees are not often grown from seeds because the seed could be anything...any variety and all sorts of odd combinations. So, don't expect to get the same kind of apple as the seed came from!
I'd assume make sure it gets lots of sun, the soil stays moist but not wet, and eventually start exposing to the outside when it's time to harden. I think you can keep an apple seedling in a pot for a few years, but it'll need to be a decent sized pot eventually. :)
(If you want to grow apple trees to produce, you'd be much better off grafting!)
Most wild apple seedlings can make good apple jelly. You can even use hard, fully grown but green apples for this. Easiest jelly ever! No pectin, nothing, good to use for adding to other fruits as a pectin substitute. Absolutely delicious spread on a plain biscuit and topped with seasonal fruit and whipped cream.
Grow little seedling! Grow! Actually, it's best if you can get it in the ground as soon as possible, early fall before the cold weather if you are in that kind of area, or all winter in milder areas. Little seedlings put down better roots than larger trees. Give it a few years before fruiting, and don't have high expectations for fruit quality. Commercial apple trees are always grafted and are clones of each other, not open pollinated. But some mighty tasty varieties are used for cross pollination! In my Grandpa's "ranch" near Yakima, the "Apple Capital of the World" (or used to be) the Golden Delicious trees had one branch of Winter Banana grafted onto one in every 20 trees. Come November, oh my! the Winter Banana apples were kissed by frost, sweet, crunchy and delicious. Now I see that variety in the stores, but I am mightily spoiled and they are a disappointment compared to my grandpa's. Your little seedling will certainly be a hybrid of the purchased variety and the variety used for pollination, often not one sold commercially. Apple trees are super-forgiving if you want to practice fruit tree pruning, or if allowed to grow naturally will eventually make great climbing trees for little ones. This is why we tolerate the sapsucker-pocked, apple-maggot-and-coddling-moth-infested tree in our yard. Apple trees can be rotting for decades and still have a long life ahead of them. They are fabulous trees!
Give me a few minutes while I caffeinate.