10) Charisma = babies.
Any time that you put a couple into the same living quarters (or a random female and male), they are going to start having babies, and will continue to do so for as long as they are there. However, the higher their charisma, the more babies they will have and the faster those babies will come.
9) Keep the pregnant women pregnant forever!
If you want to do this, the way to do so is to start getting the women pregnant when the vault is already completely full. They will never give birth; they will simply stay pregnant forever. If you zoom in on the rooms that they are in, then they’ll complain that they can’t start a family unless there is more room.
8) Select breeding partners based on their SPECIAL stats.
Any couple will give birth to kids with slightly boosted SPECIAL stats, and the boosted stats will be based on those of the parents. Put a specific set of two parents together based on what you want their special stats to be. Make their kids have kids when they become adults to keep the SPECIAL stats jumping up!
7) Build the more advanced resource buildings later on in the game after you unlock them.
Sell the old buildings if you need to in order to make more room for them. Build the Nuclear Reactor, the Garden and the Water Purifier in order to make more power, food and water respectively. Build the Nuka-Cola Bottler in order to make more food and water at the same time. Get more dwellers in order to unlock more rooms.
6) How to get more dwellers rapidly
Use the radio stations to attract random dwellers out from the wastelands, and breed dwellers in order to make more. Use the time lapse cheat in order to make baby dwellers grow up into adult dwellers very quickly so that you can put them to work. And use the same cheat to make the Radio Station attract people a whole lot more quickly.