Tips and Tricks
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 go for supplies first. You need food and water, especially water. Find it first and you can avoid dehydration, which is a threat if you have to move long distances in search of a big city, for instance.
Small towns aren't worth your trouble and could leave you dehydrated, so check the map and find the bigger cities. Of course, bigger cities also mean more zombies, but it's better to run that risk while earning great rewards than it is to lose everything scavenging some tiny hamlet that yields nothing of interest.
Although zombies can run as fast as you can, they often won't chase you for 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 great as an offensive measure of sorts, 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. 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. That way, you'll take less damage. Finally, do keep in mind that guns make noise and they could attract unwanted attention from additional zombies, so take that all into account.