I have an interior water leak into the driver's compartment of my 1996 Oldsmobile Achieva.

On the passenger side floor??
it is one of two things
1 drain tube for air conditioner is plugged up is an easy fix find the tube on the right hand side firewall and blow into the tube with an air compressor to clear the tube
or the heater core is leaking

I had a similar problem. Whenever it rained, water would leak into the interior behind the driver (driver's side passenger floorboard). Literally after 2 weeks of looking for the leak (and taking almost the entire interior apart), I found the problem. My leak was coming from two sources. The first was under the windshield wiper where in the corner where the front left quarter panel attaches to the interior chassis. I had to remove the front left wheel well splash guard, clean the current seal at the corner and caulked it with 100% silicone caulking. My fist attempt failed, but after using an entire tube and sealing everything and everywhere there was a connection, it finally solved that leak. The second was a bit easier to repair, but harder to find. The fresh air intake is located just under where the passenger side windshield wiper attaches to the car. There is a little plastic piece used to cover the fresh air intake. I caulked the connection between the metal bracket used to hold the windshields wiper and the plastic piece used to cover the fresh air intake. Apparently, over time, the original caulking failed and it just needed to be re-caulked. I would advise you to remove the front seats, remove the carpet, and the underlayment, and allow the carpet and underlayment to dry-out in the sun, otherwise the car will eventually smell of mildew. Good luck! I hope this helps!

Gm has a service bulletin on this problem. The problem occures when parked on a slope water drains into the interior, this is from a design flaw in the car. The dealship will install a small rubber tube that fixes the problem, its under the wiper arms.