Shabbat rest was defined biblically as a prohibition against anything connected with building the Covenant. There are 39 acts which are banned, some of which are less relevant in modern day Western society:

Ploughing, Sowing, Reaping, Sheaf-making, Threshing, Winnowing, Selecting, Sifting, Grinding, Kneading, Baking, Sheep-shearing, Bleaching, Combing raw material, Dyeing, Spinning, Inserting thread into a loom, Weaving, Removing the finished article, Separating into threads, Tying a knot, Untying a knot, Sewing, Tearing, Trapping, Slaughtering, Skinning or flaying, Tanning, Scraping, Marking out, Cutting to shape, Writing, Erasing, Building, Demolishing, Kindling a fire, Extinguishing a fire, The final hammer blow, Carrying in a public place.

Note that from these we can interpret things for the modern day. If we do not create a spark (kindling a fire), we don't turn on lights, and most Orthodox Jews have timers on their lights for the duration of Shabbat.
However, sometimes these can be overlooked, as in the case below:

Rabbi Chisda and Rabbi Hamnuna said that it is permissable to make plans for good deeds on the Sabbath; and Rabbi Elazar said that one may arrange about alms to the poor on Sabbath. Rabbi Yochanan said: One may transact business which has to do with the saving of life or with public health on Sabbath, and one may go to synagogue to discuss public affairs on Sabbath. Rabbi Jonathan said: One may even go to theatres or circuses on Sabbath for such a purpose. And in the school of Manasseh it was said that one may talk about the future marriage of one's children on Sabbath, or about the children's education, or about teaching them a handicraft, for the Scripture forbids 'your business', but G-d's business is permitted.

Above all, though, comes the sanctity of human life. If, to save someone's life you require to break one or more of the Sabbath laws, then you must do so, for the human life is far more precious.