There is no fixed move number that marks the start of the endgame — it is defined by material and piece activity rather than a move count. A useful rule of thumb is that the endgame has begun once the queens are off the board or each side has only a few minor pieces and pawns left, since the king can then step into the center without much danger.
Endgame technique rests on a handful of recurring ideas: the opposition and key squares in king-and-pawn endings, the rule of the square for passed pawns, cutting off the enemy king with a rook, and converting a material edge without allowing stalemate or a fortress. Basic endgames like king and queen versus king, king and rook versus king, and the Lucena and Philidor rook endings are considered essential knowledge for every improving player.
Many games that look balanced in the middlegame are actually decided by who understands the resulting endgame better. Studying endgames tends to have an outsized effect on results, because the same handful of patterns — oppositions, triangulation, breakthroughs — recur constantly across otherwise very different games.