Some guy on Sup Forums spoiled the new movie.
2034, 10 years after the epilogue of X-MEN: DAYS OF FUTURE PAST, and the world has been reduced to a post-apocalyptic dystopia after an all-out war between humans and mutants toppled the United States government. Weapon X was then reactivated to destroy the mutant race through which any means necessary, and most of the X-Men have died in the crossfire, attempting to end the conflict.
Logan is one of the sole survivors, and lives in an isolated cabin in the Canadian wilderness, haunted by the fractured memories of both timelines and blaming himself for erasing one nightmarish future only to create one perhaps even worse. He claims that "Wolverine" is dead and refuses to use his claws.
One day, a group of mutant resistence fighters led by Iceman shows up at his doorstep. They've intercepted a convoy transporting Weapon X's new asset from their main base of operations to one of their outposts, and need to deliver it to Professor Charles Xavier, who is stationed in Mutant Town, a mutant foxhole. The path there is tortuous, and Logan is the only one who knows how to outmaneuver the dangers that await them on their way back to the United States.
Logan is reluctant, until he learns the asset is X-23, a clone created based on his DNA by Weapon X's sponsor, the Essex Corporation. Shortly afterwards, a group of Weapon X enforcers led by vicious and sadistic Captain Knox attack Wolverine's cabin. Iceman's men are slaughtered, and Iceman sacrifices himself to bid Logan and X-23 enough time to escape into the wilderness.
Knox and his men pursue them, and Logan realizes, based on his own memories, that there is a tracking device embedded in X-23's arm. He slices it open with a machete, pulls it out and uses it to lure Knox and his men away. He finds a cave for them to hide and spends the night comforting X-23 as she heals from her injuries. Knox and his men burn down Logan's cabin and order all exits to the town to be closed.