Well basic strategy indicates you avoid the mouth region at all costs. other than that, Zombies are pretty pathetic. Grab whatever's available, chair, game controller, TV, and aim for the head.
After that you proceed slowly, clearing each room as you go. stock up a back pack in case you have to run, check the phones see if they're working. attempt contact with the uninfeced. Decided if your house is securable, if not, head for a place that is. remember, one bite is all it takes. You see your friend bitten, you take him out. Gather any weapons you can along the way. Small firearms are next to useless, anything less powerful than a shotgun, don't bother much. You need to destroy the entire head for a normal zombie. Bludgeon weapons are your best bet if you can find bladed ones. chainsaw is classic, but slightly impractical due to the need for fuel. My recomendation is an aluminum baseball bat or golf club. Leave the house only if the coast is clear.
Upon contacting uninfected, do something deliberate. I know at this point you'll be shell shocked and confused, but if you don't want your ass shot for looking pale and bloodstained, start singing. I don't care if the most embarassing song in the world is on your mind you sing, or dance, or juggle, anything to show them you are not infected. You and your partner should have an understanding. You are not going down together. You both need to understand that you don't have to out run a zombie, you have to out run each other.
Now we assume you have made it to a group of uninfected. as a group, try to keep conflicts to a minimum. To many times a powerstruggle within the group leads to a collapse in defenses, and the screwing of everyone. Listen to ideas carefully and seriously consider the merit of all of them. No one has died from hearing a stupid idea out, but many have from not listening to a good idea.
Securable locations. the Ground Floor is for corpses. my recomendation is to find a highrise with a well secured lobby. You barricade the hell out of that lobby and door. a heavy duty door will help you immensely. note that heavy duty means should be able to stand up to twenty people charging it. a lock as simple as a key will work, do not get doors with riot bars or handles. Knobs people, knobs. Zombies are dumb, they really can't operate anything more complicated than... well, they can't really operate anything. but if you have enough of them slamming against something... well, that'll do the trick. Make sure you secure the hell out of that ground floor, even though you plan on spending no time there. Venture out only when absolutely necessary. The buddy system is a must, it gives the zombies someone to swarm on so you can get away. There is always room for more if you have a properly equipped shelter. I know what you're thinking, why take more? Well, chances are less than a percent of a given area is going to be left, and that means there will be plenty of food for anyone living that comes knocking at your door.
Lastly, lets be heartless. There are no pets. There is only "sources of fresh meat". I'm sorry, but desperate times and all that. you will need protien. There are no friends, only allies that make great bait and think the same of you. You are not going to repopulate the earth with that hot chick who showed up yesterday, she's just another ally who might happen to be able to provide you with "stress relief". Don't make any long term plans for her, you might have to shoot her tomorrow, but you'll always have playboy.