I am trying to build a pool on top of a plane, the pool goes below the plane, How can I remove the part of the plane that is in the pool?
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You can Tab into Edit mode on the plane and use the Knife tool to trace the part of the plane that you want removed. Press K to activate the knife tool and left click to create points, to close a shape, simply left click on the starting point. You can also use right click to cancel a cut if you make a mistake.
Confirm the cut with Enter and there should be a hole in the plane.
Another way you could do it is with the boolean modifier. Basically you would place the modifier onto the pool and set the floor plane as the target object. Then, set the operation to difference. And it should work! (I haven't tested it, so tell me if it works without flaws).
One of the advantages of using a boolean modifier instead of the knife tool is that it is dynamic. You can move the the pool around and it will cut through the floor no matter where you put it. And you could simply apply the modifier if you wanted it to be permanent.