Worship is almost taken for granted on this day, at least in most Christian traditions. The early church seems to have originally gathered on Saturday in the synagogue as well as the first day, Sunday, in homes. In time the church separated from the synagogue and for the most part we have met on the first day, the day of resurrection, ever since. There is a lot of debate about everything I have just stated but it is generally followed by most historians and theologians, excepting those committed to the Sabbath, or seventh day (Saturday). Mainstream churches in the East and West follow the Sunday celebration, with some churches now providing a Saturday evening service time. (According to Jewish time Saturday evening is the beginning of the first day!)
The ancient church had a marvelous term to describe the new day, calling it the "eighth day of the new creation." That sums up a lot of the theology behind the change from Sabbath to the Lord's Day. We worship in the new age, the new creation, on the "Eighth Day."
But worship itself is a complex phenomenon which cannot be easily captured or expressed in a single, simple definition. It is a response of adoration evoked in a person who has encountered God and his presence. It is also a grateful rejoicing of those who have experienced God's grace in their lives. And, consequent to these observations, it is a set time for formal services, or rites and ceremonies, in which people gather to worship and follow a way of life.
A right view of worship incorporates all of the truths in the previous paragraph. And it stresses that worship expresses and mediates the divine-human encounter in a relationship. Underlying all of this is a presupposition that there is an understanding of God and human subjectivity in all worship. Worship implies a human subject who desires a relationship with God who will fulfill this desire if sought properly. Christian worship believes that the true God is sought and found on the basis of Christ's mediation and intercession. In him we find God's complete self-disclosure, a meeting place for true worshipers. Worshipers are brought to God in him and gather in his name, or his authority.
Forms of Christian worship vary but the central truth is this: We seek God the Father in and through Jesus Christ his Son by the power and help of the Holy Spirit. Liturgical rites, or the ceremonial parts of gathered worship differ, but true worship must always be rooted in the central truth of the triune God.