I had a '92 Corsica that had that problem, it was the weather stripping along the door that was causing the problem. If it doesn't seal properly, or if the weather stripping is coming loose in some place it won't work as well as it should.
Many Ford escorts have that problem from a leak where the rain water is not draining completely from cowl area and dripping into the vent system around the blower fan on the passenger side. I also saw a Chevy cavalier with a wet floor from the a/c condensation not draining & it was overflowing into the passenger area.
Our 1999 Grand am had a small pinhole in the floor allowing water to come up under the carpet. Pull your carpet back a little and take a water hose spray under floor boards see if you can see water coming in.
well many of the older cars have drains from the vents they can be difficult to locate but look at the bottom of your wind shield and remove the plastic cover that covers the air filter take a vacuum a suck it all out pour a glass of water in there well not into where the blower motor is just at the base of where the filter was a see if the water drains out if not the drain is still plugged and that is how the water is getting in it floods the compartment and backs up in to the motor shroud and in turn leaks out onto the passenger side floor so try an air hose or just keep on vacuuming until you find it good luck
check sunroof for leakage
better check your heater core.
you left the window open stupid!
Windshield seal? Lower door seal? Hole in floor ?
You probibly have a bad heater core.
It probably has a leak in the heater core.
Assuming that the window is rolled up, you must have a bad rubber door seal on the passenger side.
Check to see if your floorboard is rusted through. If it is patch it.
You have a leak. Possibly the drain lines are stopped up or the leak is at the windshield.
If it's the front passenger side ,I would say your heater core is leaking .
the wet side is where the sun cant get at so its rains there and doesnt really dry