Have you checked out chesskids.com? It's supposed to be for older kids, but I've used it for ideas. I think that's the site anyways...
My ds picked up chess pretty much on his own so I didn't really need anything special to teach him. But when he started to play dd wanted to play. She was 3. We did the Rook's pawn hunt game series. You can do it if you know basic moves. Both players set up their rooks where they are supposed to be, then they can put their pawns anywhere on the board. You take turns moving, regular movement rules apply, and see who can capture all the other player's pawns first. Pawns cannot move. Once they've mastered that game, move to bishops...then knights...ect.
The only things you need to know to play are how to set up the board and how the pieces move. Once you/they know that, then you can get into how many players like to control the 4 middle squares as soon as possible, the special moves, common opening moves...stuff like that. All of this stuff is super easy to find online.
There are also sites that you can play against the computer on. There are no other people so you don't risk exposing them to any bad language or the like. We have a pop up blocker and don't use any messangers so we don't have to worry about anything else coming up that we wouldn't want them to see.
My ds loves to make up games with the chess board and pieces. Being a little anal myself, I was less than impressed with this (he knows how to play...why's he doing that???), but then I talked with the high school chess coach and he said it's a great thing for them to do to help with their strategy. He said to especially encourage games where you can practice the ending. Like you have just your king and he have his king and two rooks and see how many moves it takes for him to checkmate you. Then next time have him try to beat his record.
Have fun!
