Regularly study your Vault-Tec literature, as the Perk Chart that accompanies your Pip-Boy is the key to augmenting yourself for the better. When you increase a level, you receive a Perk Point. This can be saved, or you can spend them immediately, in one of three ways:
Perk Points can be spent on raising any attribute (so you can unlock another level of perks).
Perk Points can be spent on purchasing a new perk, providing the value of the associated attribute has been reached. A few perks require you to be male or female.
Perk Points can be spent to increase the rank of an already-purchased perk. Perks can have between one and five ranks, denoted by stars on your chart. Rank 1 is always accessible (providing your attribute requirement has been met). Rank 2 and higher requires you to be a particular level.