The two negotiating skills that I consider most important are stepping into the shoes of whoever is on the other side of the table and always being willing to walk away.
I learn as much as I can about the party I am negotiating with and the asset we are negotiating over before getting deep into the process. I want to be able to anticipate how the other party will react to any counter-offer that I make. It is also helpful to know about any other parties that are negotiating over the same asset.