How can I stop a water leak in my basement?
We can only guess at this point, but one theory is that when it rains, you have water seeping down the outside of your foundation until it hits the footer, at which point it's seeping into your basement. 

At the point where you have this puddle, what is outside? Is there a gutter downspout there? Or perhaps the ground is sloping towards your house at that spot? Check those things first.