The pizza stone has to be preheated to a certain temperature to work and that often means leaving the oven on for quite a while before you begin to cook. Always place your stone in a cold oven and then turn the oven on. The purpose of this is to allow the stone to absorb the heat evenly. Once the stone has reached the required temperature then it is far too hot to handle with a conventional oven glove. Remember that you are working with a fire brick! If you place your cold pizza stone (no matter how expensive it was) into a hot oven it will very probably not withstand the thermal shock and it will shatter.
The best tool to get a pizza stone out of the oven is a pizza paddle which is a large wooden handle that looks like a paddle which slides underneath the pizza and can bring the stone out. The biggest drawback in familiarizing yourself with your stone and your oven will be how much cornmeal to dust on the stone before cooking. Too little and you will never get the pizza off the stone.
Part of the trick of using a pizza stone successfully is to season it properly. In this context seasoning a pizza stone means ensuring that when the oil seeps into it, it is cleaned so that it encourages a non stick patina which can only be acquired over time. When you take it out of the oven, place it on a heat resistant surface. I use another cold tile and let it cool down naturally. Never let your hot stone come into contact with cold water, that can make it crack