This is a topic dear to me. I have one daughter and another child on the way. My theological community places a great emphasis on children and their participation in the community. We do not place them in a special category, they are already–by virtue of God’s grace (Psalm 22:9) and by being born in a Christian home (I Corinthians 7:14)–in the only category that exists in the church, the righteous ones. In the assembly there is wisdom to be imparted and the mysteries of the gospel are revealed each week as we eat and drink and commune with one another and our children.
In light of this, our children need to treated with a new perspective; they need to be viewed with new eyes. Biblically, the gathering community is elevated to the heavens to the presence of her Lord when they meet together (Eph. 2:6). Christ summons us–by His Spirit– into His presence so we may feast with Him at His table and in the Holy of Holies. Worship is heavenly and our children need to be trained from the earliest days to see worship as heavenly. They need to be active participants in this heavenly worship. They need to see models of this at home, so they may partake of this joy at church.
Training little ones is no easy task. It requires a theological commitment that is a minority view in our own day. It is looked down upon in most evangelical churches (and sadly, in most reformed churches). Circumstances dictate much of our practices, yet, no circumstance should take away the necessity of training little ones in the home. This can be done in several ways. There are three common practices in our household that embody what I have been arguing. These are significant and necessary features, but by no means essential in every detail.
First, prayer needs to be modeled at home. Every meal is prefaced with: “Child (name), let us pray to God and give thanks to Him.” Children must understand that the life of faith is a life of thankfulness. God in His rich mercy poured out all blessings on us. He has given us His Spirit and His Son for our benefit and for our salvation. Children who are catechized in this context of thankfulness grow up to be appreciative of all God’s good gifts.
Second, singing needs to be central as the background of any covenant home. I am not speaking of random music or even music that purports to be Christian; rather, I am speaking of music that is uplifting, whether dance-like or meditative music. Classical music is to be preferred above many styles, but it should not be the sole choice of the Christian home. Children need to be exposed to a diversity of music. In my opinion, the best music for covenant children available is the music of Jamies Soles. This is Christian music that is not afraid of the hard or the obscure passages. Jamie’s music actually reflects the words of Paul that all Scripture is given for our instruction, and we may add, our singing.
Finally, family worship is indispensable. Whether five or ten minutes a day, every family needs to do it. If it is unattractive at first, keep pressing on. Family worship, like church worship, is a maturing process. No congregation sings Psalm 45 (in the Cantus Christi) successfully the first time. In our congregation, it took at least three tries before we mastered this divine psalm. In the same manner, worship is hard. Parents can seek many models available. In our home, we follow the similar pattern of Sunday morning worship. In fact, we keep our Sunday bulletins and use them throughout the week (see an example here). We begin with a salutation (Daddy: Jesus Christ is Risen! Mommy and Children: Jesus Christ is Risen Indeed!) and then kneel for confession (see an example of a confession in the bulletin). We all rise after kneeling and hear a word of assurance from God’s word that our sins are forgiven in Jesus’ name (see Romans 5:1). Typically that is followed by a reading from the Scriptures. The passage will most likely be the text for the coming Sunday sermon (our bulletin provides the reading for the following week). The reading is followed by a hearty, “This is the Word of the Lord! Thanks be to God!” Then, I choose a hymn or a psalm (one advantage of the Cantus Christi is that it includes about 100 of the 150 psalms). Usually–as the father–I will lead our family in a prayer for our needs and the needs of others. We always begin by exalting God for Who He is and what He has done. At this point, my 18 month-old knows that when daddy says amen it is time for the doxology. We raise our hands together as a sign of adoration and conclude with praise to the Father, Son, and Spirit. All this takes approximately 5-7 minutes. It is not overwhelming, but incredibly rich in substance.
You begin to train your little ones with new eyes; the eyes of faith that sees that their worship is pure worship before the Father of all glory.
is known for its excellence. 
