In Scripture the Sabbath was mostly connected with the Jewish observance of the Sabbath as beginning at sundown on Friday and ending at sundown on Saturday. it was meant from creation to be a day of rest, following the example of God himself.
At the beginning of the New Testament period, the true meaning of the Sabbath was lost in the midst of the many restrictions placed on the people by Pharisaical law. If you recall, Jesus expressed anger towards those Jews who were more concerned with keeping the day than helping someone in need. To put the Sabbath in perspective, Jesus said: "The Sabbath was made for man, not man for the Sabbath" (Mark 2:27). In other words, the Sabbath does not overshadow our responsibility to love our neighbor.
Because the early church was comprised mostly of born again Jews, the observance of the Sabbath remained important, but Paul regarded such strict observance as a yoke of bondage from which Christians had been set free (Gal. 5:1). Over the next two centuries the early church fathers agreed that the Sabbath observance in the strict sense of the law was not binding on Christians.
The "Christian Sabbath" view is the one we follow today. This view, which holds that Sunday is the Christian Sabbath, emphasizes the divine institution of the Sabbath at the close of creation. God's blessing and sanctification of the seventh day is taken to mean that he intended one day in seven to be observed by all people in all ages as a sacred day of rest and worship.
The other view today is the seventh-day Sabbath view, help by the Seventh-Day Adventists, who hold that Christians are obligated to keep the seventh day of the week as the Sabbath.
In truth, it doesn't matter if you observe the Sabbath on Saturday or Sunday, as long as you are intentional about setting aside one day for the Lord. John Parsons at Hebrew for Christians (a very nice website, by the way) makes that point when he writes, "We are called by Scripture to both remember and to guard the Sabbath Day, in order to consecrate it as a day devoted to the things that matter most in our spiritual lives before the LORD."
Then there are there is this promise from God. Even though he was directing this to the Jews, it applies to everyone who desires to please and delight in the Lord:
"If you keep your feet from breaking the Sabbath and from doing as you please on my holy day, if you call the Sabbath a delight and the LORD's holy day honorable, and if you honor it by not going your own way and not doing as you please or speaking idle words, then you will find your joy in the LORD, and I will cause you to ride on the heights of the land and to feast on the inheritance of your father Jacob" (Isaiah 58:13-14).