As time passes, Fallout Shelter progresses, and you'll need to keep an eye on things in order to progress through the game.
Once supplies have been produced you'll need to tap on them, and when workers can level up, you need to take a look for their stats to increase.
Most things will happen automatically, but of course, things can't progress unless you're there to keep watch.
As you make your way through the game, your early progress will mainly be dictated by the missions you have available to you.
Missions will include tasks like having a certain number of inhabitants, pregnancies, or stocks of water, power and food.
These will have lunchbox and cash rewards which will lead to more expansions and items, so of course complete missions as quickly as you can.
Best for the job
You'll have a variety of characters and inhabitants before you know it, and they each have their own tasks they'll be best at.
Experiment by putting characters in different positions and seeing how productive that area becomes. Once you find the right job for a character, they'll be way happier and much more productive.
You might need to put characters in common rooms or change where they stay occasionally so they don't get bored or depressed, but once they've found the right job for them, they'll usually stay put.
Characters will get experience for a variety of activities, like just working and producing items and supplies, but also for successful rushes and defeating enemies.
If there's an emergency in a room, you can send characters from other rooms in to solve the problem and earn experience from it.
Once characters are ready to level you'll need to check them individually for their stats to increase, as mentioned, so keep checking in on them!
You will need three essential supplies for survival in the vault; water, power and food. The bare essentials. These are delivered by water refinement plants, power plants and diners.
Keep characters in each and they will work towards more supplies, and you can tap on them to collect them, refilling anything you need.
You can Rush too to speed things up, but things get risky and this can cause emergencies, like radroach invasions or fires.