The goal, obviously, is to get one of your Vault Dwellers to level 10. To do this, your Dweller needs to preform a task. This can simply be working in one of the many rooms in the Vault. This process is pretty automatic. You put them in a room, they work, and you occasionally click on them to level them up. To level them up quicker, you can send them into the Waste Land. However, you'll need to keep an eye on them, as they are likely to loose heath and die.