To start the game, you first have to create a character (obviously). There are a few different character classes to choose from: Military, Science, Civilian, or simply begin the game as a zombie. The class you pick determines the skills you begin with, and the cost to acquire other skills later on.
I recommend choosing a Fireman (Civilian class) to start with. Doing so allows you to begin fast and effective zombie slaughter immediately. This means achieving higher levels very quickly, and then, as soon as you get Melee Weapons Training and Body Building, you will be practically unstoppable.
After the extremely speedy character creation process, you're introduced to the city of Malton (link to map), which consists of 100 suburbs. Each suburb contains a 10 X 10 grid of buildings inside of it, making a total of 10,000 buildings to explore (it's a big game). Once you start the game, your first turns can be crucial. Many a newbie have started the game as a cop with 12 bullets, used them on the first zombie they saw, and then were forced to create a new character. For most classes, the best thing to do is to go searching for supplies in the right sorts of buildings. (Hospitals carry first aid kits, Police Stations carry guns and ammo etc.)
There are several ways to gain experience in the game. The most obvious is to damage (and hopefully kill) zombies. Unfortunately, when beginning the game this option isn't really available to you. If you're a NecroTech employee, then the best thing to do is to use your DNA Extractor on every zombie in sight. If you're a doctor, then it's easiest to heal as many people as you can find. Once you have at least 100 XP, then you can purchase a new skill and move up to the next level (which doesn't really mean anything special).
Game play is governed by Action Points (APs). Every action costs APs, from barricading a building to spray-painting a wall. Even speaking costs 1 AP. Some actions even require several APs. You begin the game with 50, and regain one every half an hour. It's when you get low on APs and are about to log off that the game really gets interesting. When you log off, your character doesn't: it stays in the game in the same place on the map that you left it in. This means that logging off while standing outside is almost sure to get you killed within a few hours. Finding shelter is fairly easy, as you just need to find a barricaded building to enter, and then you should be fairly safe. As a note, after 3 days, your character disappears from the map, but will reappear as soon as you log back in.
Thankfully, death, as mentioned earlier, doesn't mean the end of the game. After dying you become a zombie, ready to terrorise your former comrades among the living. Playing as a zombie is quite different to playing as a human. Prey is generally harder to find, you only have a few attacks and HP aren't really an issue as when they get reduced to 0, you can just stand up again at the cost of 10 action points. Although zombies don't really need to find shelter, in order to avoid the ever-deadly XP-draining headshots, or the simple annoyance of having to stand up again, your best bet is to simply find an empty building. You can also find another crowd of zombies to stay amongst (zombies are nameless, all you see is "x zombie(s)"). Thankfully, zombification isn't permanent, as you can be revived by anybody with a revivification symbol.
Despite the length of this review, I've only begun to scratch the surface of this deep, constantly expanding game. Further information and help can be found in the FAQ and the superb Wiki. Something that really surprised about it is the huge, extremely active community. The forums are constantly abuzz with news of mobile zombie hoards and unprotected buildings full of humans. There are even a number of 24-hour mailing lists run by fans to inform zombies and humans alike of the latest events, and big XP opportunities. As a note, it's probably not a good idea to mention where you're currently situated or anything like that in the comments.
Even if this sort of game isn't usually your thing, I'd thoroughly encourage you to give it a go, as it's an extremely original and absorbing experience.
I'd also like to take this opportunity to wish a happy birthday to my friend Dougal, who is a huge fan of this game (since I couldn't be bothered with getting him a real present).