What happens after Ragnarök?

Most gods die during the battle together with the evil and the two people are left to repopulate the world. The Children of Odin addresses the event in an easily comprehensible way:

What said Odin to the Gods and to the Champions who surrounded him? "We will give our lives and let our world be destroyed, but we will battle so that these evil powers will not live after us." Out of Hel's ship sprang Fenrir the Wolf. His mouth gaped; his lower jaw hung against the earth, and his upper jaw scraped the sky. Against the Wolf Odin All-Father fought. Thor might not aid him, for Thor had now to encounter Jörmungand, the monstrous serpent.

By Fenrir the Wolf Odin was slain. But the younger Gods were now advancing to the battle; and Vidar, the Silent God, came face to face with Fenrir. He laid his foot on the Wolf's lower jaw, that foot that had on the sandal made of all the scraps of leather that shoemakers had laid by for him, and with his hands he seized the upper jaw and tore his gullet. Thus died Fenrir, the fiercest of all the enemies of the Gods.

Jörmungand, the monstrous serpent, would have overwhelmed all with the venom he was ready to pour forth. But Thor sprang forward and crushed him with a stroke of his hammer Miölnir. Then Thor stepped back nine paces. But the serpent blew his venom over him, and blinded and choked and burnt, Thor, the World's Defender, perished.

Loki sprang from his ship and strove with Heimdall, the Warder of the Rainbow Bridge and the Watcher for the Gods. Loki slew Heimdall and was slain by him.

Bravely fought Tyr, the God who had sacrificed his swordhand for the binding of the Wolf. Bravely he fought, and many of the powers of evil perished by his strong left hand. But Garm, the hound with bloody jaws, slew Tyr.

_{The Children of Odin}

The text goes on many deaths take place. Together with the gods, the evil also dies, which is what Odin was striving for.

After Ragnarok:

Deep in a wood two of human kind were left; the fire of Surtur did not touch them; they slept, and when they wakened the world was green and beautiful again. These two fed on the dews of the morning; a woman and a man they were, Lif and Lifthrasir. They walked abroad in the world, and from them and from their children came the men and women who spread themselves over the earth.

_{The Children of Odin}

But some of the gods survive as well:

Other survivors of Ragnarok included some of the gods, particularly Odin's brother Honir, Odin's sons Vidar and Vali, Thor's sons Modi and Magni. Another of Odin's sons, Balder, was revived from the dead after the battle.

_{Ancient Mythology}

The surviving gods talk to each other about Ragnarok:

Gods. The runes told them of a heaven that was above Asgard, of Gimli, that was untouched by Surtur's fire. Vili and Ve, Will and Holiness, ruled in it. Baldur and Hödur came from Hela's habitation, and the Gods sat on the peak together and held speech with each other, calling to mind the secrets and the happenings they had known before Ragnarök, the Twilight of the Gods.

_{The Children of Odin}