If this happens all the time and not only in a rain storm, a wet passenger floor is probably caused by a leaking heater core. The heater core channels engine coolant inside for use heating the interior. There may also be excess condensation (fog) on the inside of the windshield. Those with experience will note the odor of engine coolant in the interior of the car. Unfortunately, the repair is not cheap, and shouldn't be tried by most amateurs. While the part is relatively inexpensive, the labor is likely to cost several hundred dollars, because replacement requires removal of the dash.
If this happens only in a rainstorm, and seems to be water only, the door gaskets are suspect first, followed by any areas in the firewall where hoses and wiring pass through. Be sure the door gaskets are clean and free of crimped, nicked, or dry-rotted areas. As gaskets age, they might also shrink in length and loose contact with their channels, particularly where they turn, or develop a space where they are spliced, usually at the bottom of the door. In certain cases, even water that enters at the top of the door can run down into the floorboard.
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