One of the main Fallout shelter game mechanics is to produce enough food and water. Without food your dwellers will lose health, without water they will take radiation damage (the red bit on their health bar). If you’re running low you’ll need to either increase production, or lower usage.
Increase production
Build merged rooms
It’s best to use merged room first and then upgrade later. 1 large diner/cafeteria, 1 water treatment and 2 power plants is usually a good starting ratio. You can build them 1 segment at time, taking care to not expand too quickly.
Upgraded rooms may produce more, but also have the problem of taking longer to produce resources if you don’t have the dwellers (see room stats below).
Sort dwellers by room stats
Dwellers have SPECIAL stats, the rooms will tell you which is the preferred boosting stat. The diner/cafeteria requires dwellers with high A (agility), water treatment plant requires dwellers with high P (perception), power plant requires dwellers with high S (strength).
Assigning dwellers with the correct stat will decrease the time it takes for rooms to produce food/water. This is important for increasing production and essential when you start upgrading rooms.
Look to boost key dwellers stats
You can boost stats by assigning clothing, the increased amount will show as blue on SPECIAL. For example the Handyman Jumpsuit will add +3 Agility, the armored vault suit will add +3 Perception.
Once you get to 30+ dwellers consider training a few at a time in various training rooms for agility, perception and strength. A few levels with the right clothing will speed up production.
Lower Usage
In most cases you probably have every dweller working already, and struggling to make enough food and water. Put some out into the waste to explore, this will reduce usage and bring in stats improving clothing as loot.
If you have a large vault with a lot of unused rooms then you probably have a lot of dwellers in power plants. Consider deleting some rooms short term so you can reassign dwellers from power plants onto more urgent tasks. This will give you time to work on improving dweller stats.
Growth and Efficiency
Don’t grow too fast, children consume food and water, this can be a drain if you’re not ready for it. Good dweller stat management, and steady dweller training make the difference.
You should be able to feed and water 50 dwellers with 2 fully upgraded power plants, 1 fully upgraded diner/cafeteria, 1 fully upgraded power plant.