If you don’t keep your workers and children fed in Frostpunk, they will become hungry. Discontent may rise slightly, and hope may also fall. If you don’t solve this situation fast, people will begin to starve.
If people are starving, then discontent will rise massively, and hope will still be falling. Eventually, workers will die which will set off a whole chain of other problems. Complaints about the lack of cemeteries and so on. It’s a hard thing to recover from.
Therefor, I recommend having your food be sorted as fast as possible. Once you have food rations available, residents will go ahead and eat it automatically when they have some free time.
If you wish, you can check out some more Frostpunk Guides here.
How to get food
There are two components to food, Raw Food & Food Rations. When you first start a scenario, you will already have some Raw Food available in your stores. You can check near the top of the screen, on the right hand side of the temperature button.
First, we need to turn these raw pieces of food into actual rations that your workers can eat. To do so, we need to build a Cookhouse. Build one, connect it with some streets and assign some workers. These workers will convert the raw food into rations that people can eat.
To actually get more pieces of raw food to cook later, we need hunters. You can build hunters huts straight away. Assign workers, who will go out at night and hunt for food. At the start, they will bring in around 17 raw food per day. You can build as many hunters huts as you please, as it will bring in more food.
There are some laws and technologies which you can look into to increase food production in Frostpunk. Although they aren’t completely necessary. For example, Food Additives or Soup in the book of laws allow you to feed your workers for less. Although this will greatly increase discontent, and not really worth it.

I do recommend that you research into Hunters Gear and Hothouses eventually, using the workshop. That way, you can increase food production massively without having to sacrifice too many of your workers.
Otherwise, you can create an Outpost, where outpost teams will transfer food to your city daily. You can find out more about that process here.