Rule #1:
There are always more zombies.
There's more dead people than living people in the world, and the zombies are always making more. Remember this every time you think you've cleared a place out. Remember it every time you think you are well-off enough to bunker down and wait it out. Remember it every time you think you have enough ammo. Which brings us to...
Rule #2:
Save the last bullet for yourself.
If you can no longer be part of the solution, at least avoid being part of the problem. Knowing you've saved a bullet for yourself may also comfort you (however slightly) if you have to use one on someone else before they become something else. It's also probably a lot better than getting ripped apart by the undead hordes, if it comes down to just you and them. Although, if it comes down to just you and them, chances are someone has failed to follow...
Rule #3:
Survival takes teamwork.
Seriously. It doesn't matter who you were in the days before the end, the only distinction worth anything now is zombie or survivor. Everyone who is still alive needs to look out for each other and, just as important, stick close to each other. If you have to go to the bathroom, your whole team should be waiting for you right outside. You should be sleeping in shifts in the same room. You should never run off alone to check out a noise. Separating from the team at any time could mean the end of you. If you see something you think would come in handy, everybody can go over to check it out with you. On your own, you could easily find yourself surprised and surrounded by shambling revenants anywhere you go because of...
Rule #4:
No place is zombie-proof.
The best you are going to be able to hope for is zombie-resistant. No matter how fortified you think your location is, you can't stay in there forever because of Rule #1. That means that even if you've unwisely decided to stay put somewhere, you're still going to need to venture out from time to time for food and supplies, which means you and your fellow survivors run a constant risk of exposure. Maybe someone doesn't tell you they were bitten because they're afraid, or maybe they were exposed through an existing injury and don't even know it yet. Either way, that's an unexpected zombie in the clubhouse right there. And let's not forget that any opening that can admit something zombie-sized eventually will - zombies are implacable, indifferent to discomfort, and do not get tired. They'll find their way in eventually. Besides, you'll want to keep moving around to keep your supplies up, because you should be following...
Rule #5:
Zombies are not the only threat.
Sure, zombies are terrifying abominations, but they're no more deadly than a gangrenous wound or a case of food poisoning or an uncontrolled fire. Remember to look out for zombies, but don't forget to look out for everything else - it's a dangerous world out there, and the undead have torn down all our defenses against it with their lifeless hands. Remember: you're no good to the rest of the living at the bottom of a frozen lake or buried under the rubble of a school. Keep your eyes open and your mind sharp, keep your supplies up, make sure your water's fresh and your food properly cooked, and take a supremely conservative approach to exploring new places. The last thing you want to do is make the zombies' job easier.
Good luck and always be ready!