I'm glad you started this thread coz i just happen to be an expert of zombie survival.
First thing you do is assess the nature of the outbreak. Consider things such as the amount of zombies loose, the concentration of zombies in the area, and whether or not the nation is doing anything about it.
Once you have considered those factors, look for an appropriate place to barricade yourself in, or, if your area if the outbreak in your area is too severe, you may need to move to a safer location. One of the most important things you have to remember is safety in numbers. Stick with your friends, family, and pretty much whoever isn't a zombie. However, picking some random to stick with may not always be a good idea as that person might backstab you to save himself/herself so try to get people fairly trustworthy.
Next step is to find yourself some supplies, if your chosen area you wish to barricade is a convenience store of some sort, which I highly recommend, then supplies wouldn't be much of a problem. But, if it's not, you'll need to look for such items as bean bags to pile, wire (preferably barbed), canned food (those that don't require cooking may be a good idea), a supply of clean drinking water if you don't already have access to it, a radio or portable TV and things most people tend to forget: batteries and a can opener. Anything else you might find in a hardware store could be useful. Be creative.
Depending on your situation, you may want to perform this step before the previous one but I'll leave that for you to judge. Considering it's relatively hard to find firearms in Singapore, I highly recommend long, heavy, blunt objects to use as weapons. A perfect example is a golf club or bat. Knives are no good as you'll have to get in close to a zombie to kill it and getting close to a zombie is not a good idea as they could easily bite you and pass on the infection. When in combat with one of the undead, remember to aim for the head as the only way to destroy a zombie is to damage the brain. A few bashes to the head with a golf club would easily do the trick. If you think you've killed a zombie but it's brain is still intact, don't be fooled as you have only incapacitated it for a limited period of time. To be absolutely safe, destro its brain even if it's lying on the ground seemingly dead. But remember, only use your weapon as a last resort. Zombies are extremely slow and it's always better to run away than to fight. Do not engage in close combat unless absolutely necessary i.e. you're surroundered or cornered.
After barricading your chosen area, be sure to leave your radio or TV on because at any time information crucial to your survival could be broadcast. If lack of batteries or power is an issue, turn your radio or TV on for an allocated amount of time at regular intervals. If you need to leave your safety shelter for any reason, never do so alone. It is crucial that somebody else knows where you are at any point in time and that you're with at least one other person. Another important thing you need to remember is DO NOT GO OUT AT NIGHT unless of course it is absolutely necessary. This is a very common and possibly very fatal mistake. Zombies are far more active at night than in broad sunlight. All activities whatever they may be should be done during the daytime. Also, if you're going to be travelling a fair distance away from your zombie shelter, be sure to bring some supplies with you as you might not be able to make it back before the sun sets and if that is the case then you should start seeking a temporary shelter for the night at least an hour before the sun goes down.
If you have any further questions please post them and I'll gladly share some survival tips with you.