If you are like the vast majority of people and don’t have a dehydrator do not despair, there are ways to do it that only need an oven.
What kind of apple to dry
You can use any kind of apple you want, but baking apples seem to hold their shape a little better then the out-of-hand apples. Apples are inexpensive so experimentation is worthwhile to find out if your favorite apple does well being dried into chips.
The key to any drying technique is uniformity of the product in this case apples. Its less important exactly how thin they are (that just changes the amount of time in the oven) compared to how uniform each slice is (they all finish drying at the same time.) A mandoline or V-slicer does that job really well, because they are really sharp so use the handguard or other protection. You could even use a apple corer-peeler but they are so think it will take longer to dry.
In commercial fruit drying they use sulfur to prevent microbial attack, we could do that but people have been drying their own fruit for thousands of years without it, so I’d skip it. It’s not like we’re making thousands of tons of it per day.
Though if you are making a large batch holding the apples slices in some acidulated water to keep the apples from browning. You need 1 teaspoon of acid (lemon or lime juice, vinegar or wine) per quart of water.
On the other hand I do like a bit of extra sweetness so a short bath in boiling simple syrup would be nice. A simple syrup is a 1:1 ratio of sugar and water and brought to a boil until the sugar is dissolved. You can also add extra flavor by dropping in a large piece of lemon or orange zest, a slice slice of fresh ginger or a cinnamon stick. Use a wide pan for this and cook the apple slices a few at a time so they don’t overlap until they turn translucent, about 1 minute. Remove and pat dry with a clean towel.
Now is a good time to add even more flavor, sprinkle on some ground cinnamon, nutmeg, allspice, ginger or coriander. Or just bake them naked.
Preheat the oven to 225°F. Most ovens are not very good at maintaining a low temperature, so I add a thermal capacitor, in my case a large cast iron griddle to smooth out the heat waves. A pizza stone would work just as well. This increases the preheat time but is worth it.
Lay the apple slices in a single layer on a baking sheet with a silicone mat on it. It makes clean up easier, but if you don’t have one start checking for doneness 5 minutes earlier.
Bake for about 50 minutes, this is very approximate since it depends on the moisture content of the apples, the thickness of the slices and the day’s humidity. The apple slices should be a little crunchy and a little pliable when done. They will crisp up once they cool completely.
The slices will last weeks in a plastic container. You can get months out of them if you all the slices to cure in a large airtight container that is only filled 1/3 of the way with slices and gently shaken every day for a week to allow the moisture content to reach equilibrium.