Observing the Shabbat is one of the major signs that identify an individual as one of the children of Yah and of Israel (Exodus 31:13-18).
People, who are not part of the 12 tribes of Israel (britam.org), become part of Israel by accepting the King of Israel (the Messiah - John 1:49) as their Master and Savior. If someone is your Master, then you obey him (Ephesians 2:11-12). The Messiah is the King of Israel and any King has laws or instructions for his subjects to follow (Deuteronomy 17:18-20). The children of Israel follow the Messiah and obey the commandments just like He did when He was on the earth (1 John 2:3-6; John 14:6; Luke 4:16; John 15:10).
The Bible gives us an idea on how to observe the Shabbat.
"If thou turn away thy foot from the sabbath, from doing thy pleasure on my holy day; and call the sabbath a delight, the holy of the LORD, honourable; and shalt honour him, not doing thine own ways, nor finding thine own pleasure, nor speaking thine own words: Then shalt thou delight thyself in the LORD; and I will cause thee to ride upon the high places of the earth, and feed thee with the heritage of Jacob thy father: for the mouth of the LORD hath spoken it." (Isaiah 58:13-14 KJV)
“Speak to the children of Yisra’el, and say to them, ‘The appointed times of Yah, which you are to proclaim as set-apart gatherings, My appointed times, are these: ‘Six days work is done, but the seventh day is a Sabbath of rest, a set-apart gathering. You do no work, it is a Sabbath to Yah in all your dwellings.” (Leviticus 23:2-3 The Scriptures)
You should not buy or sell on the Shabbat (Nehemiah 10:31; 13:15-21) and you should do good on Shabbat (Matthew 12:1-12).