Question: "When should children be baptized and/or allowed to take the Lord's Supper?"
Answer: While some churches have requirements for children to attend Bible classes for instruction in doctrine and the meaning of the ordinances before being allowed to participate, many others do not. Whatever the case may be, it is wise for parents to instruct and prepare their children for baptism and communion. Ultimately the instruction of children in the ways of God is the responsibility of the parents, and the church is there to help.
Before taking communion, the main requirement for all children (as with all adults) is that they have received the Lord Jesus Christ as their Savior. Even though some children make this salvation decision at an early age, being baptized and partaking of the Lord's Supper should not be rushed into. As a child matures in his faith and it is evident that he is truly born again, the father and/or mother should be perceptive as to when he is ready to understand and participate in communion. The spiritual maturity level of one child differs from that of another, even in the same family.
In many churches, when the parents of a child make it known to the pastor that he/she is wanting to be baptized, the pastor speaks with the child to decide if he/she is ready. This is a good and wise practice. It is vitally important that a child understands that neither baptism or communion saves him/her, but rather they are steps of obedience and remembrance of what Jesus did for us in providing for our salvation (Luke 22:19).