1.Find/Make A Group
The key to surviving the zombie apocalypse is to have a group. If you travel alone you will eventually slip up and make a mistake. You're only human. But, if you have someone to watch your back you might not end up being a zombie's lunch. Keep your group small though, because that will put yourself less at risk, and you won't need as many supplies. Rick and his group are never too large (except for a few times). You will notice, though, that at all times, whether it's Rick, Daryl, Carol, etc., that they never try to travel alone. Lone wolf < Party.
2. Make Finding Supplies Your Biggest Priority
As seen in show, everyone must do their part to go on supply runs and/or find ways to make food. The worst thing about the zombie apocalypse is the fact that supplies will dwindle fast and you have to be prepared to get what's left for you and your group. Screw around < Find Food
3. Clear Every Room
You will notice that every time one of the characters in The Walking Dead goes into a new building, or close area they clear it. What I mean by that is they cautiously check every room for the infected, or survivors. Then, and only then will they start looking for supplies. You don't want a zombie taking a chunk out of your neck while you are looking for a can of beans. Life > Beans.
4. People Are Going To Be Worse Than Zombies
We all know that in The Walking Dead the zombies are certainly a huge problem. We also know that the bigger problem is that humans are insanely more dangerous now. With the collapse of the government there really are no more laws except survival. People will try to rob you, kill you, rape you, and pretend to help you only to stab you in the back. Zombies are very predictable, whereas people can change on the fly, especially when they can basically do anything they want now. Zombie teeth < Crazy guy's gun
5. Keep Level Headed
This is actually a big one. Survival experts all agree that if you can’t keep your head straight when crap goes down then it could cost you and your group their lives. In the series, the leader of the group becomes delusional and really puts the entire group in danger. There are also several other times throughout the series where the mental health of various members of the group deteriorates quickly. Rick likes to go really crazy quite often now, and I don't think it's working very well for him.
Most TV shows over-dramatize a lot of different parts, including The Walking Dead, but it will also give you great insight if the time ever comes for the zombie apocalypse is upon upon us.