It took a lot of time. Time to heal the physical wounds and making peace with the lost of loved ones. And then it was the reconstruction.
First it was Hogwarts, as the students would return to classes just a couple of months later after the battle. There were new teachers and new rules, but little by little, year by year, the school returned to its former glory. Past was the time were the school had failed the students, were bulling and fights between houses were the everyday of the school. Academically, the school reformed its curriculum, making it the great institution of magical studing that had been centuries ago.
Then it was the Ministry, the magical goberment and the Wizengamot. New rules were passed, positions inside the Ministry were reasingned to valid and prepared individual and not the one with the purer blood or better conections. It was a long road, a slow change, but the lack of Wizengamot member of the more traditional faction to opose the new rules made things easir.
Years after the wizard world was a much save and fair place. A statue had been rised in a small island in the middle of the Black Lake, to represent all of those that died to made the world better. It was a beautiful statue. At each aniversary of the battle turned into a gathering, even Fawkes appeared to trin a sad and melancolic tune. All the survivors took a minute of silence and then started to retell how much the world had change, thanks to them. Those people might havve died, but their deaths had caused that the world that they loved was a much better place. And everyone hoped that wherever they were they were happy and proud of what they had achieved.