First, you need a Soul Shard to make the stone. That's easy enough to get. Once you've created the Soul Stone, it is now a useable item. Select yourself (or party member), and use the stone (while you're still alive). This will give you a 30-minute enchantment, where upon dying, you will be given the option to "Release Spirit" or "Reincarnate".

So, basically, no, you can't ever really use the stone itself to ressurect. You use the stone while the person is still alive, and it gives them an enchantment that lets them ressurect.