To start, you're going to need to gather a few things:
-A plastic sandwich bag
-Somewhere cold, like a refrigerator
First, you need to gather the apple seeds. Some apples may only have a couple, while others may have six or seven! I usually use four or five apples worth. Whatever you do, make sure not to damage the seeds, as they most likely won't ever grow. It's best if you cut the apple with an apple cutter, or eat the apple down to the core then split it in half with force. You can use a knife if you wish, but it might damage the seeds. Once you've gathered your apple seeds, make sure to wash any remains of the fruit so that they don't rot. I find it easiest to use a small strainer, so that you don't lose any of the seeds.
Now that your seeds are prepped and ready, you will need to prepare your paper towel. All you need to do is stick it under a faucet so it becomes slightly damp. Then you will need to squeeze most of the water out so there isn't too much moisture. Once you've done that, you can place the seeds on the napkin, and then fold it up and place it inside of the sandwich bag.
Now that it's in the sandwich bag, make sure it's sealed up and place it inside of your refrigerator. You can expect to wait up to two months before you see any signs of growth. Essentially what you're doing is simulating nature. When apples mature and fall from the tree, they decompose yet the seeds remain on the ground. Unless animals get to them first, they remain on the ground throughout winter. Once spring hits, the seeds come out of dormancy and start to sprout! Essentially, they're programmed to germinate after a period of coldness. Make sure to check on them around once a week, and if any seeds start to rot, it would be best to remove them and replace the paper towel so the rest of the seeds don't rot as well. Also keep an eye on the moisture level, if it seems a little dry you should add a small amount of water to it.
I checked on my seeds after a month, and it turns out they all sprouted! But don't be surprised if they don't before, or even after the first two months. If they haven't, it's okay! They really aren't supposed to sprout yet. Take the bag out of the refrigerator and place it in a sunny location. South facing windowsills work best, but any sunny location will do. Blow some air into it (which creates a mini greenhouse), and then seal it up.
Leave them in the bag until they sprout. They should start sprouting within two weeks. If they haven't all sprouted within a month and a half, the ones that haven't probably never will. You can pitch them if you wish, or just leave them to see if they finally sprout.