The Sabbath, when it was first given at Horeb, was about rest - rest for the weary slaves.
According to the text, to each of the three accounts of the mosaic covenant, the reason it was given was that the Israelites had been slaves and the way to remember the Sabbath, the way keep it holy was to abstain from work.
Exodus 20:
"I am the Yahweh, who brought you out of Egypt, out of the land of slavery…
“Remember the Sabbath day by keeping it holy. Six days you shall labor and do all your work, but the seventh day is a sabbath to the Lord your God. On it you shall not do any work, neither you, nor your son or daughter, nor your male or female servant, nor your animals, nor any foreigner residing in your towns.”
Exodus 34:
Then Yahweh said: “I am making a covenant with you… Obey what I command you today…
"Six days you shall labor, but on the seventh day you shall rest; even during the plowing season and harvest you must rest.
Deut 5:
"Yahweh made a covenant with us at Horeb. It was not with our ancestors that Yahweh made this covenant, but with us, with all of us who are alive here today…
And he said: “I am Yahweh your God, who brought you out of Egypt, out of the land of slavery…
"Observe the Sabbath day by keeping it holy, as Yahweh your God has commanded you. Six days you shall labor and do all your work, but the seventh day is a sabbath to Yahweh your God. On it you shall not do any work, neither you, nor your son or daughter, nor your male or female servant, nor your ox, your donkey or any of your animals, nor any foreigner residing in your towns, so that your male and female servants may rest, as you do. Remember that you were slaves in Egypt and that Yahweh brought you out of there with a mighty hand and an outstretched arm. Therefore Yahweh has commanded you to observe the Sabbath day.
It wasn’t until the Second Temple period that the priests started the practice of worshiping on the Sabbath. Before that, the Sabbath was all about rest.
But, what exactly is work? As is typical, there is something lost in translation. The words used in the commandment translated as work primary mean occupation or assigned task.
Consider these words used in the original text and their meaning:
In Deut 5:
taabad is translated as “labor”. It means: To work, serve. To labor for another. To till the ground. To compel another to serve.
melakteka is translated as “your work”. It means: Occupation, work, business. Public business.
melakah is translated as “work” and is a similar to melakteka. It also means: Occupation, work, business. Public business.
So, the commandment could be translated:
“Observe the Sabbath day by keeping it holy, as Yahweh your God has commanded you. Six days you shall labor in your occupation - your business, but the seventh day is a sabbath to Yahweh your God. On it you shall not work at your occupations, neither you, nor your son or daughter, nor your male or female servant, nor your ox, your donkey or any of your animals…”
And, indeed, this makes sense for a pastoral people: They still had to feed their animals on the Sabbath, and milk the goat and the cow, and so on. Perhaps draw water from the well. Prepare meals. Tend to one’s sick and to children. Just as people must today. But none of these things are one’s occupation, not labor for gain within a family.
This, perhaps, was a point Jesus was trying to make when he “broke the Sabbath”. According to the Gospels, Jesus was challenged by the authorities several times - accused of breaking the Sabbath. Consider that he was never accused of worshiping incorrectly. Every time he was challenged he was accused of working on the Sabbath. And every time the ‘work’ that he was doing was not his occupation - was not labor for gain.
So, based on the biblical record, generally the way to keep the Sabbath to not labor in your occupation for gain. Everything else is on the table, it would seem.
Still, exceptions must be made. We must still care for the sick (Doctors, Nurses, …) and rescue those in peril (Firemen, Police, …) and so on. In our modern society, someone also has to keep the power on. And, somewhat ironically, the Priests then and now our Pastors most significant day of labor in their profession is probably on the Sabbath.