Take your time to get the hang of the game by joining a server with a low population in order to avoid survivors. Also, choose a server with daylight, if possible (you can also find servers that vary according to likely conditions in a given region). Playing on European servers at night contributes to likely daylight conditions, or playing on U.S. servers during local daylight hours has the same effect.
Always make supplies your first priority. You need food and water especially so look for it to avoid dehydration, which is a threat if you have to move long distances in search of a big city, for instance.
Stick to larger cities since small towns may lack supplies and could leave you dehydrated. Check the map and find the bigger cities, which of course will have more zombies but it's better to run that risk while earning great rewards than to lose everything while trying to scavenge a useless little town.
Remember that although zombies can run as fast as you, they usually won't chase you for very long. You can also lose them by running around a corner and hiding in a shed or building, or just dropping to the ground (which also works well as an offensive tactic if you're carrying an ax and want to launch a surprise attack on a pursuing zombie).
Guns are by far the most effective weapon, so use them to kill. You can shoot a zombie in the head to kill it quickly. With a melee weapon, as noted above, you're best off if you lie prone so that you take less damage. Finally, do keep in mind that guns make noise and they could attract unwanted attention from additional zombies.