Does anyone have any great real estate negotiation tips they can share?

The home has been on the market for over a year. Seller lives 4 States away. I use to rent this home from her. She is an older lady and does not want her home to go to the banks. I made an offer this morning low balling 20 thousand less with a 90 day closing ( just to give me some room to haggle with). Her son will be playing the negotiation game with us... any tips to help me save a few bucks would be WONDERFUL! What has work? Thanks so much for stopping and giving me advice :)