I'd say the basic premise is to always encourage progression.
Stage 1 is to ensure they can do the basics - can they dribble and pass a football or do they know how each chess piece can move? For example, my infant son can't control his direction of travel whilst dribbling a ball, so I ignore the boundaries of the pitch.
Stage 2 is for you to demonstrate additional skills or tactics (mini-drills - in or out of game). Say things like, "look if you take my pawn this turn, you'll be able to move towards check next turn" to expose them to the basic tactics of the game. With football(soccer) this could be you demonstrating the specific part of the foot to kick with to shoot in the air or keep the ball along the ground.
Stage 3 is to provide (obvious) scenarios for your child to use those techniques. If they don't seem to take advantage, go back to stage 2 (for that element). With chess, this could be always opening yourself up to "fool's mate" until your daughter spots it and capitalises. Likewise with football, if you're in goal, leave your legs wide open to see if your child realises they can kick through your legs.
Stage 4. Once you know they have a reasonable arsenal to use against you, up your level of play to become more competitive. It's usually fairly easy to gauge when a child is getting frustrated, so avoid working them too hard. Try to keep most of the play fun for them, pushing their boundaries occasionally (depending on their age and temperament). The level can vary as they start to improve, but ideally you should let them reap the benefits (win) when they start to make leaps forward.
When they can genuinely compete, do so (Stage 5). Just remember that being a good sport / losing every so often will make you more fun to play with and will probably help to hold their interest longer-term. Even as an adult, there aren't many people who continue with an activity if they always lose against their friends - if you're obviously better you have nothing to prove.
