In order to complete this quest, the Vault Dweller needs to visit the Vault 13 library, at the far end of the southwest part of the level. Once there, they need to use the Science skill on the computers in the room.
With a successful Intelligence check, it rewards with 350 XP for researching important information. Failing the check will just produce a message about surfing the Interweb.
The skill can be used on both computers in the library, as the experience stacks.