Everyone, especially little kids, likes to win. So teach them a few easy mates, and let them get them in on you from time to time. The four and two move mates are easy to teach and have the added value of showing some strategy.
Basic Mate in 4
1. e4 e5 2. Bc4 Nc6 3. Qh5 Nf6 4. Qxf7++
Basic Mate in 2
1. f3 e5 2. g4 Qh4++
Explain Your Moves
For playing longer games versus children, it is nice to explain why you are making your moves - especially the ones which seem to have to benefit such as developing, or building a pawn structure, or waiting so that a trap is timed better. Don't do it too excessively though, it will get annoying. Usually you can tell if your move confused the kid, or if they are unsure how to respond by it.
Tell them they are allowed to have 2 takebacks per game. This will let them still feel like they are playing by the rules, but get to have a few second chances. Keep in mind, the goal is to have them legitimately win as much as possible.
Although this is not the best approach for seasoned players, it can be beneficial to tell the kids to make the most "annoying" move possible. What I mean by that is, can they force a knight to move, or block a pawn going forward, or attack the queen, etc. Make as many harassing moves as possible. This can be amusing to the player doing the harassing, and also presents opportunities to win pieces in simple situations.
Show them an opening
Go into a little chess history lesson. Perhaps show them the movie "Searching for Bobby Fischer" so that they will get interested in at least one player. Then you can transition into other famous players such as tal, Kasparov, etc. When you teach them about a famous player, show them one of their more commonly used openings. Here is one that Fischer played a lot (the first 5 moves were his commonly played opening - I thought I would include a whole game as an example):
1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. O-O Be7 6. Re1 b5 7. Bb3 d6 8.
c3 O-O 9. h3 Na5 10. Bc2 c5 11. d4 Qc7 12. Nbd2 Bd7 13. Nf1 Rfe8 14. Ne3 g6
15. dxe5 dxe5 16. Nh2 Rad8 17. Qf3 Be6 18. Nhg4 Nxg4 19. hxg4 Qc6 20. g5 Nc4
21. Ng4 Bxg4 22. Qxg4 Nb6 23. g3 c4 24. Kg2 Nd7 25. Rh1 Nf8 26. b4 Qe6 27.
Qe2 a5 28. bxa5 Qa6 29. Be3 Qxa5 30. a4 Ra8 31. axb5 Qxb5 32. Rhb1 Qc6 33.
Rb6 Qc7 34. Rba6 Rxa6 35. Rxa6 Rc8 36. Qg4 Ne6 37. Ba4 Rb8 38. Rc6 Qd8 39.
Rxe6 Qc8 40. Bd7 resign
Show them some chess puzzles
Get out a book, or an online resource (chess.com has a daily puzzle), etc., and set up some mate in one positions, or two or three depending on skill level, and go through those. There are so many, you can give out unique ones to each kid. Finding a mate is always fun, and will teach them to look for moves, or to examine moves which do not work since those puzzles, for the most part, only have one acceptable move set. Here is a smothered mate:
[fen "4r2k/1p4pp/1qn4N/2bQ4/8/1P6/5PPP/2R3K1 w KQkq - 0 1"]
I could not seem to get the move list to work in this example, the solution, as I am sure you are aware is: Qg8+ Rxg8 Nf7++.