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While only experience will allow you to survive in the long run, here's a few important tips to get you started.
Pause the game. After the Collapse feature an active pause you can toggle on/off using the space-bar, use that feature. That way you'll have all the time in the world to decide where to build stuff without your survivors starving to death.
The first thing you want to do is to find a good location for your base. The more you can reuse existing walls and buildings to design your future base, the less resources you'll have to spend on erecting new walls. Note that the furniture on the map are considered unusable, you settlers won't sleep in those dirty, irradiated beds, but they'll happily disassemble them for parts.
Secondly, build a farm immediately. It's in the zone building menu.
Don't build it too big at first. The bigger the farm, the longer it will take for your survivors to make it. Go over to the people screen and disable the farming skill for everyone but your 2 best farmers to speed up the process.
You'll also find food ingredients you can cook in your basic kitchen by razing fridges and food boxes (found mostly, but not only, in restaurants).
Most structures and recipes require metal and coal, both of which can be made from stones and wood at a forge. You should build 2 forges relatively quickly, each one dedicated to the production of each. The “Build until X units in storage” option is very useful here.
You should also setup a Trading Zone quickly, it's free and traders won't show up until you have one. Just make sure it's not in an enclosed space.
Rain collecting barrels are the only way to collect water until you get the masonry tech. Research masonry very early (probably first) and then build a water well to replace them. Dirty water should be boiled at a campfire to make it non risky to drink.