One of the few times that I got in trouble during church was when my friend and I were joking around during communion. My friends dad walked right up the center aisle to the front row where he and I were hunched over, choking down our giggles, and grabbing each of us by an ear he trotted us right back up that aisle and out into the foyer. Needless to say it wasn't a pleasant experience. Our parents may have let us get away with some restlessness and even the odd giggle but there was never any tolerance during communion. You are a parent! In our church tradition we expect you to be the primary spiritual director for your children.
Helping your child to know when it is OK to participate in the communion is one of your responsibilities. When they are very young (ie: 3-7 yrs old) and happen to be in a service where communion is served, let them know that they are not old enough yet to partake of it. Use the incident to create discussions after church about communion. Give them something to look forward to as a sign of the maturity. I would recommend saying something akin to, "When you are old enough to explain to me the significance of the communion and what it means then we will discuss your ability to take it with us." Read together with them the passage in 1 Corinthians 11 about how upset Paul was when he learned how thoughtlessly the Corinthians were partaking of the communion. Especially point out that Paul says we are to use discernment and self-examination.
Many parents deal with 'comparison anxiety' - the worry that other parents are doing it differently and you may be seen in a negative light. Overall, I can only encourage you to remember that ONLY YOU are responsible for your child. What do you do when your child says, "But dad, Billy gets to take it!?" You simply say, "That's between Billy and his parents."
With great joy you will come to a place where your child is old enough and can understand it. This is when you get to talk about whether or not they have invited Jesus to be their champion and their leader. Once you have ascertained that your child has indeed accepted Christ then you can invite them to take the communion with you. Perhaps you'll want to invite your child to sit in the service with you the next Sunday that communion is served so that they can take it with you? Or you can explain how we can celebrate it as a Christian community at any time and even plan a family communion service (as long as the little brothers or sisters aren't going to stage a protest). :)
Guiding your child into their first communion will set the stage for the next milestone in their spiritual journey - Water Baptism.