I have been thinking about this for the past 10 years, and even taught my little sister over and over when we were younger. Just in the the infinitely small chance it might happen.
This is a post made partially out of fun, and partially out of preparation in case it does happen. Meaning you'd want to download it to a local device. I'll try to leave a downloadable PDF at the end.
There are about 10 steps you need to be aware of, and honestly depending on the circumstance there may be a bit of changes. For example there is a common trope in the zombie-movie fans out there, that if you were in the apocalypse "could you survive"? They always ask: Are they FAST zombies, or SLOW zombies? Which is honestly a valid question. Factors like that we can't account for, but would make for a really different experience.
Step 1: Find a Hiding Spot
This comes first because you need to gather your thoughts, composure, and make sure you are not in the way of a big crowd. That crowd being either of zombies, or of people trying to escape (who will inevitably become zombies due to noise).
Keep in mind this is just temporary, and you'll need to refer to this action plan to figure out what to do next.
Step 2: Find a Weapon
You need to be able to defend yourself, and this step honestly might happen when you find a spot in the Step 1. However this needs to be your next priority if you haven't found a good one yet. Maybe two considering how many zombies you'll probably be beating away.
Find a pipe or big ol' wrench, a nailed up baseball bat, etc. Even better if you can find a firearm in this case.
Step 3: Find People
You can't be alone during an apocalypse, not only will you go mad, but you need other survivors for the greatest chance. Now you're not going to be creating a community right off the bat, but someone should take point. Preferably the most calm individual, or the one with the most experience with zombie games! ;)
These people can watch your back when you're not looking, and also help you carry more resources.
Step 4: Find a Vehicle
Now this one may have to be based on your judgement, for one traffic might have caused things to standstill. Another issue is the noise, as it will only bring in more zombies. You'd be surprised how quickly they can damage your vehicle, since they have no self-preservation mechanism.
However if you can find something quiet, fast, or just out of desperation need one. Then by all means.
Step 5: Find a Base
Now after playing State of Decay for so long it has gotten me to look at real world locations in a different way. I see buildings as potential outposts, or maybe even bases. You wouldn't want a public library for example because of the sheer size, and the maintenance alone would eat you up. You'll have to think about how many people you will have with you.
Find a medium sized place, such as a restaurant with walls around, or a small motel. Something preferably already fenced in, and then fortify that.
Step 6: Find Food and Water
I think in previous iterations of this list, this was two separate steps. However we are going to need both, and while water takes priority; Where there is water, there is probably food nearby.
You'll want to find things that won't expire quickly, and find ways to prepare for when food runs out. Honestly think about an airfryer maybe if you have enough protection in your base. Little energy usage, and mild noise.
Step 7: Pick a Leader
While I have a variety of opinions on this step I'm going to go with how State of Decay put it:
A Builder: Someone who prioritizes defenses, and creates safe zones for travel.
A Sheriff: Someone who protects the group, while also handles disputes in the communities as a whole.
A Warlord: Someone who prioritizes offenses. Pushing back the line of defense against the zeds, and putting other enclaves in their place.
A Trader: Someone who establishes a connection with other enclaves to create a trade network. If someone is camped out a food site, while another is at the firearms store, then a trade connection can be made.
Bonus: The Polymath. You're honest best bet is to incorporate all of these. Being economic is very helpful, if there is other enclaves of people out there. However having the tenacity of a warlord, the composure of a Sheriff, and the futureproofing of a builder, are all still important.
Step 8: Build Outposts
Your base isn't your only place of residence, as you'll need to create a web of outposts as well. They can be sources of water, food, materials, fuel, and more. Not only that, they can also be places of interest. Perhaps a secondary base of operations, if the primary is too far away from your current goal.
You're gonna need power and water, so maybe finding a way to take control of the water tower, or a local power substation.
Step 9: Find More People
This should be a little earlier on the list, but if you don't have a variety of benefits like power or resources, then they won't join you. Find ways of making your base enticing to them, not just because it will make them safe. It will give them a home.
You'll want to be careful and vet whoever comes in. You don't want them to steal your stuff and go, but you also don't want to be untrusting either.
Step 10: Survive
This little guide is meant to help you gather a foothold, nothing more, as we don't know what it would be like. When you find that out, and discover what caused it to happen in the first place; Then perhaps we can take steps to turn it around.