This is a brief article (paraphrased from the Doom 3 video game strategy guide) which gives a few quick yet useful tips on how to not get killed by zombies.
1: Be Patient
First of all, you can't simply "run-n'-gun" in a zombie apocalypse. Survival requires strategy, observational skills, and most of all, patience. When entering an area for the first time, proceed slowly and cautiously. Listen for and anticipate approaching zombies.
Sudden attacks can scare the hell out of you and cause you to make stupid mistakes. Your best weapons are your wits. Keep them about you at all times.
2: Take Cover!
Unless you've got some good protective armor or decent fortification, you're not immune to bites and scratches, which means standing out in the open during zombie fights can be a very bad idea.
Conceal as much of your body as possible to minimize the risk of being bitten or scratched. Hide behind corners and doorways so you only have to deal with a few at a time. Take cover when you need to reload. Back up through doors and take out zombies as they follow you through.
Standing still while fighting zombies is risky. Standing still without any cover between you and them is downright suicidal.
3: Rounding Corners
Here's a simple trick that could save your life. When you approach a blind corner, stop before the corner, face the corner, and then run around it. That way, if there's anything nasty waiting for you around the corner, you're already facing it.
Just because zombies often lie in wait for you doesn't mean you have to face them on their own terms. For example, if you're relatively certain you're going to be attacked when you enter a room, go into the room and run forward to lure them out of their hiding spots, and then backpedal and take them out as you retreat to a more defensible position.
This tactic works especially well when you can back into a hallway to escape zombies that are attacking from the front and sides. You can frame them in the doorway and blast them full of lead. This also prevents being surrounded and becoming overwhelmed.
To play it even safer, you can also make noise or throw rocks and junk in their general direction to lure or distract them as you plan an effective strategy for taking them all out.
5: Let There Be Light
Sure, there's something unsettling about exploring dark areas with one hand carrying a light source, but blindly stumbling into a zombie attack is very dangerous. If you get jumped while using a light source, at least you know where your foes are.
Always, always, always use a light source to explore all dark areas. You'll discover zombies lying in wait, and you'll find hidden items that you would have walked past otherwise.
6: Kill Everything!
Unless you have a good reason not to, take out every zombie you see. They can open doors, climb up ladders and over walls, and break through whatever fortification you have if it isn't strong enough. They are absolutely relentless, do not get tired, and aren't hindered by pain. Most of them are smart enough to follow you into other areas, where there are probably even more waiting. The best way to keep from being overwhelmed is to deal with zombies as they appear.
If you must flee, never run ahead, but back to a previously cleared area. Running into the unknown will only draw more heat than you are prepared for.
7: Ammo Management
Stupid mistakes can cost you your life. One of the dumbest (and easiest to avoid) is letting your weapons run out of ammo. Reloading in the middle of a battle is extremely risky. Get into the habit of reloading your weapons after every firefight, and make a mental note of your ammo reserves. Stand still while you do it so that you don't attract the attention of more zombies.
However, it's also possible to reload too frequently. After a fight, take a couple of seconds to make sure that nothing else is coming before you reload. You don't want to be thinking you've killed everything in the immediate vicinity, reloading your weapon, and then jumped by a zombie while you're off guard.
Get into the habit of counting your rounds. Ensuring you reload when your magazine is empty, but a round remains in the chamber will give you one emergency shot if you get jumped mid-reload.
Also, conserve ammo by using melee weapons whenever possible.