In desperate times if you need a quick recovery, you can find food, water or power inside a lunch box at random. Save the lunch box until you need a boost in your resources, just in case. If your resources are well-managed, though, you will not end up needing any lunch box boosts at all, and you’ll often see your resource bars get to the maximum.
There is a chance you can find resources outside of the vault. What you have to do is send one of your dwellers into the wasteland. The longer that they stay in there, the better the chances that they will find something good. However, if they stick around too long the chances increase of them dying. So don’t let them stay in there too long.
If you want to get rid of a low-talent Dweller to make room for a high talent Dweller, then place only that Dweller into one of the production rooms, then rush the hell out of it. Rush it over and over and let the rush fail. Let them try to fight the fire on their own, or fight the Radaroaches on their own, and their health will go downhill. Keep doing this until they die. Then don’t revive them.
If one of your rare or special Dwellers dies in a fire or a Radaroach attack, or in any other sort of attack, you can revive them simply by using bottle caps. If you want to place a Dweller in an area where they will have high amounts of talent and a big effect on the food, water or power, then drag them over to where you want them to go and they will automatically displace the Dweller with the lowest amount of talent.
Be sure to keep your vault door upgraded. The vault door is the gateway to the rest of it and if you don’t upgrade it, it will be a whole lot easier for it to get attacked, and for your resources to get raided. Keeping resources is just as important as getting them in the first place, so protect them with smart defense.
Pay attention to the stat boosts that various clothing add to characters, and equip them with the clothing depending on where they are located. For example, if a suit boosts Agility by 5, then you want to equip it on someone who is working at the Diner. If it boosts Strength by 3, then you want to put it on someone who is working at the Power Generator.