The movie likely picks up a year or two after Civil War. Ulysses Klaw attempts to sneak into Wakanda to steal vibranium (something we know is totally up his alley from Age of Ultron). Everett K. Ross is tracking Klaw for the CIA and follows him into Wakanda, only to be found and threatened with death by Klaw's crew. Black Panther then steps in to save him, dispatch with Klaw's men and capture the thief. This leads to the interrogation scene from the first trailer and the scene in this trailer where Ross is confused and then amazed at what he learns to be the truth of Wakanda.
Before they can do anything, though, a masked Killmonger breaks in and springs Klaw from his restraints. We find out that Killmonger and his parents were exiled from Wakanda when he was a baby for their politics, primarily against the Royal Family. He's seen as an outcast primarily, but is still somewhat close with Shuri, BP's sister and a top engineer/scientist, whom he grew close to during their shared time together at MIT.
Killmonger's plan is to recruit Klaw to get money/muscle/access so that he can mount a coup in Wakanda and take the throne for himself, promising the thief a ton of vibranium once he's assumed power. Killmonger tricks Shuri and is able to steal a prototype Panther suit (the gold one we see in the trailer) to overpower T'Challa. Luckily, the young king is saved from true harm by the Dora Milaje, but the interaction leaves him uncertain and spiritually injured. He turns to the advice of his ancestors and former Panthers in the Land of the Dead, giving him the clarity and focus to defeat Klaw and Killmonger, cementing his worthiness as warrior and king, and returning Wakanda back to safety. All is as it was, save one detail - T'Challa decides to go public with the truth of Wakanda's splendor. The Golden City hides no longer. Roll credits.