In the endgame - as a general rule - you should develop the pieces in order of the strongest fitst (king, queen to pawns last)
Also, Recognising key patterns are important to ensure a speedy win or warn you of immanent danger so that you can act accordingly. During Endgames you are on the look out for Mating Patterns. I shall list some here - you should memorise them all through practice - it will seriously improve your game.
3+ pieces
- Horwitz bishops ( Queen & Rook & [-2 bishops])
- Greco's Mate (Queen & Bishop & [-Knight])
- Back-Rank 2 Rooks Mate (Rook & Rook)
- Anastasia's Mate (Rook & Knight)
- Pilsbury's Mate (Bishop & Rook OR Rook & Bishop)
- Morphy's Mate (Bishop & Rook)
- Boden's Mate (Bishop & Bishop)
- Double Bishop & King+2 Bishop's Mate (Bishop & Bishop [&King])
- Blackburne's Mate (Bishop & Bishop [&Knight])
- Bishop & Knight Mate (Bishop & Knight [&King])
- Corner Mate (Knight & Rook)
- King & 2 Knights Mate (Knight & Knight & King)
1 (possibly defended) key piece
- Queen Mate (Queen)
- Epaulette & Swallow-Tail / Gueridon's Mate (Queen)
- Damiano's & Damiano's Bishop Mate (Queen)
- Max Lange's Mate (Queen)
- Dove-Tail / Cozio's mate (Queen)
- Lolli's Mate (Queen)
- Back-Rank & Box Mate (Rook [&King])
- Anderssen's & H-File Mate (Rook)
- Opera Mate (Rook)
- Arabian & Hook Mate (Rook)
- Reti's Mate (Bishop)
- Phillidor's Legacy / Smothered & Suffocation Mate (Knight)
- David & Goliath Mate (Pawn)
*Remember - all moves that use a rook / bishop can also be done with a queen (however the reverse is not true -as some moves requiring a queen can only be done by her)