Teach him English first. It will be a lot more useful to him than chess. Then, when he is a little older, he will be able to read chess material in English if he is still interested.
Help me teach my kid (5yr)

Play blitz to acquaint the player with actually moving pieces; classical games are too long for children. Blitz is fun; what makes it fun is by constantly moving pieces instead of staring at them. Besides, blunders are funny and make it all enjoyable. Keep it light and fun, not serious and heavy. Your local chess club probably has a Fascist president who is too serious for the club's good. The other members of the club probably don't feel that way. To exclude is wrong and you talk to the other members about it and have this absurd policy stricken. Don't let him control you.
Really great that he's interested and i'd agree that it seems daft that the chess club won't let him get involved. Is it that they aren't allowed to supervise such young people due to regulations? If so perhaps you could also attend at the same time. I agree that perhaps you could apply some pressure on the club... or just tell them he is 7!! I found the lessons on the chess.com app were pretty useful - it lets you think about what to do in each situation (hopefull the same is available translated into your first language. Anyway - sounds like you're doing a great job. Maybe i should send you our 2 year old...!
Thanks everybody! I'll phone the chess-club again, try to find out the reason why they won't allow it. Didn't seem that weird to me to have an age limit, but apparently it's not that uncommon for young children to join.
Your kid must really understand what is winning all about. To win you need to checkmate your opponent. So I suggest give him 2 or 3 easy mate problems to solve everyday. You can repeat the problems, so he will get familiar with the pattern. Before you ask him to solve a mate problem, show him first basic mate positions. If it is already more than 15 minutes, and he can't still see the solution, show him the solution.
Teach him also basic tactics like pin and fork. Ask him also to solve easy pin and fork problems.
A good source of tactical problems for his level is World's Champion Guide to Chess by Polgar.
Teach him also two rooks against a lone king mate. One Rook and a King against a lone king mate.
Ask him to castle to make his king safe. Put his rooks on open file. Develop his minor piece in a good square.

This book contains no text, just lots of positions to solve and the early ones should be easily accessible to a young player.
http://www.amazon.com/Chess-5334-Problems-Combinations-Games-ebook/dp/B00DWK544C/ref=sr_1_1?s=books&ie=UTF8&qid=1459455607&sr=1-1&refinements=p_27%3ALaszlo+Polgar
If solving puzzles is fun to him, a book like this may be helpful (I think you can click (click on the "Look Inside" link to see the format of the book.. you will have to scroll a out 1/4 of the way down to get past the introductory material on how the pieces move. It is mostly mating problems, but will touch on all of the common tactical motifs. There will be thousands of mate in one puzzles followed by mate in 2, 3 etc. Or if you prefer computer software, I think something like "Chess Tactics for Beginners" from chessok.com might be useful. If he's really taking to it, having a head start on tactics and finding mating patterns will be useful when he turns 7 and can go to the chess club. Then you may want to get a coach for him if he really appears to have a long-term interest.
Minor update:
He's still playing happily. We've come up with fun names for his weird openings (e.g. the "pawn crusher" or the "lopsided threatener") and I'm trying to work in some of the more conventional openings. As somebody pointed out, getting him to focus on checkmate will be key.
The local chess club will allow him to participate after all, and I think it will be nice for him to play against other kids.
I've ordered the polgar book (maybe I'll get my puny rating up in the process )

Try the spanish opening, then "fried liver" (dont ask me why its named that way).
Spanish opening:

I wholeheartedly second TheTexans recommendation of the big black book. I used it with my 5yo and it's great.

However it is worth noting that kids need a system for when they get overwhelmed, which will be often.
I've ordered the polgar book (maybe I'll get my puny rating up in the process )
What Polgar book did you get. It's nice that you get that book. Majority of kids do enjoy solving easy tactics problems. Set up the problems in the board as it will be visually more enjoyable for them when they solve problems in a board.

Try the spanish opening, then "fried liver" (dont ask me why its named that way).
Spanish opening:

Hi,
I could use some advise in how to proceed with teaching my kid.
He has been playing chess for a couple of weeks. We've gone over the basic movements quickly and he knows all the moves (including castling and en passant). He plays the chess.com bot on my phone a lot and he wins consistently on setting 2 without hints, his strategy usually involves a pawn rush, promoting one or two pawns and then a long endgame with as many queens as he can manage. I think he is more interested in the patterns and shapes of the positions than actually winning. When we play on a real board I always let him remove pieces from my side before we begin.
I've checked out the chesskid.com site, but instruction is in English (not our native language, so the videos make no sense to him), and the local chess club doesn't allow children under 7 unfortunately.
Any tips or suggestions?