The endgame is the time when there are less pieces on the board, generally not including pawns. The role of king safety begins to lessen as pieces exit the arena. The king in turn often becomes a more active force.
Generally you want to trade down into an endgame when you are up substantial amounts of material as this ensures a simple victory. Naturally you don't want to trade into an endgame if you are losing, and perhaps will avoid a queen trade if you are a rook down as you want to try to keep the position as complex as possible hoping for your opponent to make a mistake.
Below are some key endgame tips.
1. Keep your eyes out for tactics
As pieces come off the board long empty files, ranks, and diagonals are as exploitable as ever.
2. Try to get a queen or two.
One of your main endgame plans should be to advance your pawns to get an extra queen or two. After you are up a major piece (Queen or Rook) if you don't spot an immediate checkmate you should attack your opponent's pieces and use a critical endgame checkmate pattern.
3. Use your king.
This is especially true when you only have less than 3 pieces left on the board not including pawns. When only a few pieces are left on the board your king can play a much bigger role in the endgame for both offense and defense without having to worry about getting attacked as much.
4. Trade Pieces When You Are Ahead in Material, but Avoid Trading Pawns
Below is an extreme case from a beginner game. White is up a piece and thus should be able to easily take black's last few pawns and get a queen to checkmate. However he traded pawns and ended up simply reaching a drawn game.
Here Black correctly uses this concept and goes into a critical endgame checkmate pattern.