How can you stop water from coming out of the cement basement floor when there is excessive rainfall?

Get it sealed. Concrete will weep moisture because its very porous. There are many different kinds of sealants out there and your local home improvement supplier will tell how you the best kind to apply. You paint it on like normal paint and it will make the concrete look shiny like a varnished piece of wood. This is due to the ground water wanting to rise back up through the floor.