Legend of Korra takes place almost a century after Legend of Aang. Korra is the next Avatar, and is being taught by Aang's son, Tenzin. She's already learned Water, Earth and Fire, so now she's learning Air.
Aang's spirit will also make an appearance in the show, but not until the final episode of season 1 (OMG, spoilers!), along with flashbacks involving Aang, Sokka and Toph.
So, yeah. Aang, Sokka, Katara, Zuko and Toph bring peace to world, team build Republic City, world builds Aang statue, Aang teaches son airbending, Aang, Sokka, Toph and Zuko die, Korra born, Korra teaches herself Water, Earth and Firebending, Tenzin teaches kids airbending, Korra moves to Air Temple, Tenzin starts teaching Korra airbending, Korra visits Republic City.
The rest will be in later episodes.
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