Zombiesm seems to affect your brain, making you move more slowly and more aggressive. It also seems to cause necrosis of the whole body. There is no known cure.
Since it is transmittable by biting, scratching and other open wounds, it seems to be caused by a virus, bacteria, or parasite. In some movies, however, they tried antibiotics, but they didn't help, which means it has probably evolved a natural protection against them. That could only have happened if they have been exposed to antibiotics, so we could assume that it started in a populated, advanced area.
I'd avoid any such area, so I'd move away from any major city. Meanwhile, scientists would start to work on a cure, in a similarly isolated area. If it were possible, I'd try to find them.
Otherwise, find weapons. Guns would be relatively effective at killing zombies, but they would leave rotten, microbe-infested corpses lying on streets. A better choice would be using flamethrowers to kill the pathogen as well. That, or explosions
In the long term, I'd try to make use of the chaos to get my hands on some equipment to help me escape the planet. After disinfection, a spacecraft would be great. It's (very) unlikely, of course, but possible to steal a rocket or something and dock with the ISS. It would be safe until we'd run out of resources, when we'd have to go back to the surface.