Here is my installment of the apple breeding series which deals with planting the seeds. Written version below.
Apple seeds generally require stratification in order to break dormancy and begin growing. Think of stratification as a clock or timer of sorts. After accumulating X number of hours below a certain temperature, the seeds believe they have gone through winter and it's okay to grow now. Stratification is not difficult. If you harvest the seeds in the fall and put them into cold storage, then they will be ready to plant in late winter or spring. Apples which are stored in cold storage must certainly contain seeds that are stratified enough to be ready to grow too, but I haven't tried it. I would assume so though. The other option is to simply leave the seeds outside. You can sow them in the open ground and let the cold weather work on them, or you can sow them in flats and put those outside. Whatever you do, I don't think you need to think about it too much. I haven't, and it works well for me. Just keep them cold when up until you are growing them out.
I like to start mine if rich flat mix in the greenhouse in later winter. Anytime between about the end of January and the middle of Feb is good. Later is okay too, just don't wait too terribly long. The flat mix I use is 2/3rds of old flat mix, with 1/3rd new sifted compost. I just keep the same stuff cycling year after year. Some of the mix gets planted out into the beds when plants are transplanted out into the ground, but the new compost addition each year replenishes that. I use this same mix for all my vegetable starts and most everything else that I pot up. I also add some handfuls of coffee grounds and wood ashes, and if I have it, oyster shell flour. It's good stuff and grows great seedlings! For more see my old blog post on planting flats and flat mix.
The seeds are stored in small plastic bags, labeled with their identity, see the video on that step here. I like to use some sawdust in the bag to moderate the environment. Sawdust also has some antimicrobial properties, unlike paper. Don't use paper! The sawdust should be damp, not wet. If the seeds begin sprouting, that is just fine, just poke a hole and stick the root down in there. the unsprouted or barely sprouted seeds I plant 1/2 inch deep. If the seeds are dry, I can't tell you much, because I haven't grown out dry seeds, so you'll have to look elsewhere for that information.
If you are new to growing seeds in general, it is important not to over water or the seeds and seedlings may be attacked by decay. Some say that the surface of the soil should dry out between watering. Just don't let them dry out too much and don't keep them sopping wet. You should however water them well the first time, but then allow the flat to drain and dry for a few days. As long as the soil is moist, the seeds should be okay. Roots like air. A damp mix with air space is ideal, not a wet mix where all air space is filled with water like a sponge.
You can also plant the seeds in the open ground. Just prepare the site well first and put a layer of fine material such as compost, coffee grounds, sawdust, etc.. over the bed surface to prevent the crusting that is caused by rain and water. That way the seeds can come through easily and the exchange of air in the soil will not be unduly hampered.
After getting a healthy start in the greenhouse, the seedlings are planted into a nursery bed outdoors to grow for the season. I would say the ideal time to transplant them varies by their progress and the weather. I think anything between 2 and 3 inches tall is pretty good, but they can be transplanted earlier or later depending on the weather etc. If they are to be grown in pots, especially in a greenhouse, they can be transplanted when very small, if care is taken, at almost any time really, but I'd probably wait till you have at least a couple of true leaves on them.
One parting warning. Almost every spring I have mice in the greenhouse, and almost very spring they eat some important plants before I remember that this happens every year and set traps. This year, the first night I lost about 15 of the already sprouted seeds, including most of the Cherry Cox x Sweet Sixteen seedlings and a bunch of the Sweet 16 Wickson crosses. Now I have 3 traps set and have killed 3 mice in 4 or 5 days. Next year maybe I'll remember to do that pro-actively! Same thing happened last year. :-/ With multiple traps and good bait (roasted bay nuts for me, but almost any roasted nut or nut butter is good) it is almost entirely preventable.
That's it for now. I'm sure we'll revisit these seedlings when it's time to plant them out in the garden.
I will am getting my first blooms this year, so in all likelihood, we'll have some fruit to look at later in the year. Isn't that exciting! Who knows what will reveal itself...