I'm having an issue with my power steering pump on my 1996 honda accord?
Whenever I start the car with the engine cold, I hear a sort of grinding or whirring noise coming from right around the power steering pump. I'm not sure if it is the pulley or the pump itself making the noise. And also, I have a leak problem. There's what I'm pretty sure to be power steering fluid all over the general area in which the pump and reservoir are, even over the alternator and belts which are right below it. I can't find the source of the leak. It drips down to the ground right below the pump. Also My power steering fluid inside the reservoir bubbles up when the car starts running. Anybody have any ideas on what the issue may be?
It needs a pump
The noise is being caused by air in the system. Fix the leak, refill it and your problem will probably be solved. If you wait too long and run the pump low on fluid it will probably end up being damaged.
You're correct in assuming the power steering pump is bad. It or one of the hoses can be the source of the leak.
Check the hoses for leaks, get a reman pump installed, and have the fluid flushed from the rest of the steering system.
The groaning noise is caused by the pump when there's air in the system. Air in the system means your level is too low, and it can be difficult to get all the air out even if you fill it to proper levels.
Leak? Before you do anything else, find the leak and fix it. You may have to drive the car to a car wash and do an engine degrease to clean up the oil. Then start the car and try to spot where the new oil is coming from. Then you know what needs to be fixed. Since it's a 96, it could be a worn pump seal; meaning oil can be leaking onto the pulley and then from there it gets slung all over the place, making it difficult to identify exactly where it's coming from.
Oil on hot parts can start a fire. So it's well worth the time to have the car checked by a professional. Oil on the belts can cause the belts to slip and cause the alternator to slip and not charge the battery properly and provide sufficient electrical power to the car.
Don't ignore the problem. Fix it or get it fixed. THEN all should be good for another 100,000 miles or more.
I find it truly amazing what some expect from a 20 year old car to be honest of course it will have issues. And cost l;its to put right.
Leaky connection at the pump. 
With a leak, the fluid runs out. When the fluid gets low enough, the pump starts pumping air with the fluid. It's foam. That's the noise. It's a warning that you are below minimum allowable fluid. Add some!
The problem is a leak. It could be a hose. It could be a shaft seal or housing seal on the pump, or it could be something in the rack and pinion.
These repairs are difficult for the average driver who is not a mechanic, so bring your car to several repair places, including a dealership, and get some written estimates for repair.
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