The equipment you will need is a heavy-based frying pan (oven proof), several bowls, a peeler, an oven, a knife, a chopping board, a spatula and a rolling pin if you're not using pre-rolled pastry.
Gather your supplies and pre-heat the oven to 200 degrees Celsius.
Peel the apples then halve and core them.
After peeling, halving and coring the apples place them in a bowl with the juice from the lemons. This stops the apples from discolouring.
After setting aside the apples melt half the butter in the frying pan.
Once the butter has melted add the sugar and stir it until the sugar is dissolved.
Once the sugar and butter starts to caramelise, add the apples. Place the apples end-on in circles around the pan. You need to make sure that the apples are tightly packed so they don't fall over.
Before you put the pan back on the stove, cut out a circle of puff pastry that is slightly larger than the diameter of your pan. After cutting it out place it in the fridge.
After packing in the apples put the pan back on the stove and add remaining butter (stop if the pan will overflow). Then simmer for about 15 minutes or until the apples start to become soft.
After your apples start to become soft take the pan off the stove and unscrew the handle or otherwise prepare the pan to go in the oven.
Drape the pastry over the apples and tuck in the edges. Then place the pan in the oven for about 20 minutes or until the pastry and apples have finished cooking
After you take the tarte tatin out of the oven leave it to cool for 10 minutes so that the caramel can set.
After you have partially cooled the tarte tartin, flip it out onto a nice plate and leave it to cool some more (optional). When it is cooled enough, serve it with cream, ice cream or custard.
Health and safety: Be careful when you are adding the butter as it is quite easy to make it overflow and as it is hot caramel it can stick to your skin and burn you.
Health and safety: As always, be careful when using knives and the oven. Also be careful when taking the pan in and out of the oven.
Some other things that you can try once you have got the hang of the basic recipe are adding other flavouring agents such as cinnamon or cloves or you could try it with a different type of pastry.