When you create a wellstone it appears in your bag. They do not stack. If your bag is full it will fall to the ground in front of you.
Once crafted you need to place the wellstone same as you would plant a seed. The distance you can place one from a core spring is listed in the spring info along with how many wellstone slots are available for that core spring.
Wellstones generate water just like a spring does. It takes a while to build up and you might not see the water immediately after placing the stone. Wellstones can be upgraded similar to core springs at a reduced cost for some of the upgrades and I believe less water output in general.
They are a good supplementary water source if you have maxed out your main springs upgrades, planned tree placement poorly, or wish to increase the flow rate of your epic river network.