I came upon a food blog called Smitten Kitchen-where a couple from New York takes on different recipes and posts their results, regardless of success or failure.
There I found a post on apple tarte tatin, and immediately new this was my next cooking attempt. (the recipe is also at this link-with more detailed instructions than what I will provide)
The first step involved peeling, coring, and beveling the apples, then adding sugar and lemon juice for them to emit their natural juices.
Then I prepped the caramel with the healthiest of materials-butter and sugar. (this combination on the stove must be constantly stirred-until it becomes a healthy brown color and the butter almost separates from the sugar)
As soon as the sugar has become caramel, remove the skillet from the stove, and place the apples round sided down to cook for 20-25 minutes. Make sure to continue moving the apples around, and with a spoon constantly covering the apples with the caramel sauce.
Once the apples are cooked, cut out a puff pastry round and cover the apples, tucking it in on the sides. Place the pan into a 400 degree oven, and let cook for 20-25 minutes or until the top is brown.
Remove from oven, get a plate larger than the pan, place on top, say a prayer, then flip the tart onto the plate!
Success!