The best way to negotiate down the purchase price of a home is to arm yourself with comparable sales that support your offer. Find three sales very similar to the subject property, make market based value adjustments for differences to "equalize" the comparables to the subject property and then reconcile those differences to arrive at a final value. Submit your purchase offer along with your analysis, and then negotiate vigorously for your position.
I would also recommend along with this strategy that you ask for two other ancillary items to be used as negotiation pawns; things that you're willing to concede in order to get the price you want.
For example, I recently negotiated a $41,500 price reduction for a client of mine and in addition to that, asked for a roof replacement and to refinish the hardwood floors. I didn't expect to get the roof and hardwood floors, but in the end, we got all three! You never know until you ask, and you never know the position of the seller until you negotiate hard.
I really enjoy negotiating great deals for my clients, it's one of the greatest rewards in the real estate business. Let me know if I can help!