In the article A Puritan Approach to Worship, JI Packer describes the nature of Puritan worship and their principles of practicing it.  He defines worship as doxology, a giving of glory, praise, honor, and homage to God, but more expansively, all true piety (godliness) is worship.  For the Puritans, the practice of worship includes praise, prayer, preaching, the sacraments, catechizing and the exercise of church discipline.  It encompasses three spheres of life: public, in the local church; domestic, in the family circle; private, in the closet.  Packer quotes John Owen, Stephen Charnock and George Swinnock on the topic with the last quote capturing his recommendation for how to improve modern day worship:

• If either we come (to worship) not unto it by Jesus Christ, or perform it not in the strength of the Holy Ghost, or in it go not unto God as a Father, we transgress all the rules of this worship…Acting faith on Christ for admission, and on the Holy Ghost for his assistance, so going on in his strength; and on God, even the Father, for acceptance, is the work of the soul in this worship.  – Owen
• Worship is an act of the understanding, applying itself to the knowledge of the excellency of God, and actual thoughts of his majesty….It is also an act of the will, whereby the soul adores and reverence his majesty, is ravished with his amiableness, embrace his goodness, enters itself into an intimate communion with this most lovely object, and focuses all his affections upon him.  – Owen
• God is a Spirit infinitely happy, therefore we must approach him with cheerfulness; he is a Spirit of infinite majesty, therefore we must come before him with reverence; he is a Spirit infinitely high, therefore we must offer up our sacrifices with deepest humility; he is a Spirit infinitely holy, therefore we must address him with purity; he is a Spirit glorious, we therefore must acknowledge his excellency…he is a Spirit infinitely provoked by us, therefore we must offer up our worship in the name of a pacifying mediator and intercessor.  – Charnock
• Prepare to meet your God, O Christian! Take yourself to your room on the Saturday night, confess and morn your unfaithfulness under the ordinances of God; ashamed and condemn yourself for your sins, entreat God to prepare your heart for, and assist it in, your religious performances; spend some time in consideration of the infinite majesty, holiness, jealously, and goodness, of that God, with whom you to have to do in sacred duties; ponder the weight and importance of his holy ordinances…; meditate on the shortness of the time you have to enjoy Sabbaths in; and continue musing…till the fire burns; you cannot think the good you may gain by such thoughts, how pleasant and profitable a Lord’s day would be to you after such a preparation. The oven of your heart thus baked in, as it were overnight, would be easily heated the next morning; the fire so well raked up when you  went to bed, would be the sooner kindled when you should rise. If you would thus leave your heart with God on the Saturday night, you should find it with him in the Lord’s Day morning.  – Swinnock