MiniChess is a free site for children who are just starting chess. Instead of a full game, it teaches one thing at a time: how each piece moves, how to plan a few moves ahead, and finally how to checkmate.
Don't get trapped by the poop.
Survive 15 moves against three kings.
Catch the knight with three kings.
Get a pawn past the knight.
Get a pawn past the rook.
Eight pawns each. Get one to the other side.
Get one pawn past two bishops.
Stop eight pawns with two bishops.
Checkmate a lone king with real rules and a real engine.
The trickier checkmate, with real rules and a real engine.
Learn the ladder mate, with real rules and a real engine.
Your whole army against a knight and its pawns.
Two jumping knights to catch.
One bishop, one colour of squares.
Two bishops cover every diagonal.
Keep the rook off your back rank.
Two rooks, and Black can castle.
Beat the most powerful piece with teamwork.
Two minor pieces working together.
Nearly a real game. Play carefully.
The closest thing to a full game of chess.
Start with the movement puzzles. Each one puts a single piece on the board with a goal square to reach and a few walls in the way. Solve it in the fewest moves and you'll know that piece for life.
Then try the mini games. They use only a couple of pieces each, so the rules stay small, but you play against a computer opponent that gets tougher as you level up. When you are ready for real chess, the army games give you every piece against a computer with only a few. Everything also works on a phone or tablet, and there is an Android app on Google Play.