From Jewish Encyclopedia.com: Shabbat Goy

SHABBAT GOY:
By : Joseph Jacobs Judah David Eisenstein

The Gentile employed in a Jewish household on the Sabbath-day to perform services which are religiously forbidden to Jews on that day. The Shabbat goy's duty is to extinguish the lighted candles or lamps on Friday night, and make a fire in the oven or stove on Sabbath mornings during the cold weather. A poor woman ("Shabbat goyah") often discharges these offices. The hire in olden times was a piece of ḥallah; in modern times, about 10 cents.

Both employing a goy and having candles lit on Shabbat are questionable. Approximately 18 minutes prior to Shabbat, Rabbinical Jews have made it a woman's duty to light candles while reciting the following "blessing":

From http://www.chabad.org:
"Blessed are you, L‑rd our G‑d, King of the universe, who has sanctified us with His commandments, and commanded us to kindle the light of the Holy Shabbat."
The logical conclusion is this prayer is directed to a god who commanded you to light the candles of Shabbat. Assuming it is acceptable to have fire kindled leading into Shabbat... this blessing is still, at best, incredibly misleading since it specifically excludes YHWH as the blessing's benefactor. We are, in fact, commanded by YHWH not to kindle fire on shabbat.

From http://www.shabbatcandlesticks.com/:
Actually, a search for the reason for lighting Shabbat candlesticks reveals an interesting history behind it. In fact, there is no commandment in the Torah to light Shabbat candles. The tradition of lighting Shabbat candlesticks derives from a much later period in Jewish history ... The rabbis, in order to make their point clearly, and to solidify the authority of rabbinic law throughout the Jewish community, instituted the recitation of a berakhah when lighting Shabbat candlesticks, thus implying that it is a commandment with the force of Torah behind it.
If a commandment did exist to light the candles, candles would then be lit every week without fail since it would be sinning not to light candles -- it would not be tradition. Since YHWH did not make such a commandment based on Deu 4:2 (not to add to or subtract from Torah) and Joshua 8:34 (stating that no commandments exist outside the written Torah), you could say the tradition of praying to a god who commanded it is clearly an idolatrous practice. It should concern everyone.
Deuteronomy Chapter 4
2 Ye shall not add unto the word which I command you, neither shall ye diminish from it, that ye may keep the commandments of YHWH your God which I command you.
3 Your eyes have seen what YHWH did in Baal-peor; for all the men that followed the Baal of Peor, YHWH thy God hath destroyed them from the midst of thee.

Exodus Chapter 35
2 Six days shall work be done, but on the seventh day there shall be to you a holy day, a sabbath of solemn rest to YHWH; whosoever doeth any work therein shall be put to death.
3 Ye shall kindle no fire throughout your habitations upon the sabbath day.'

Joshua Chapter 8
34 And afterward he read all the words of the law, the blessing and the curse, according to all that is written in the book of the law.
35 There was not a word of all that Moses commanded, which Joshua read not before all the assembly of Israel, and the women, and the little ones, and the strangers that walked among them.

According to strict Jewish law, a Jew is not allowed to employ a non-Jew to do work on the Sabbath which is forbidden to a Jew. The rule of the Rabbis is "amirah le-goy shebut" (i.e., "to bid a Gentile to perform work on the Sabbath is still a breach of the Sabbath law," though not so flagrant as performing the work oneself); but under certain circumstances the Rabbis allowed the employment of non-Jews, especially to heat the oven on winter days in northern countries.

To employ a goyim on Shabbat, rabbinical jews claim that only "my" servant (ie thy servant) is not to be employed -- not "my" cattle -- not "my" daughter; but it is OK if your servant, cattle, or daughter is employed. So, does your servant become my servant when your servant is asked to serve me? Another stretch of the verse is done through defining your servant as a slave that lives with you since in Exd 21:6 & Deu 15:17, a servant back then lived with their owner...

Anyhow, it is a well-known and common practice for some religious Jews in Israel to hire a Shabbat Goy to turn on and off their lights during Shabbat. Unfortunately, this risk these Jews are taking is created due to someone's belief that turning on and off lights is a form of melacha (work). Quite similar to turning on and off electricity, is getting a glass of water. By turning on and off the faucet is not considered Melacha by anyone as far as I know. So, why do people consider turning on and off lights Melacha?

Most Karaite's believe Melacha is any form of creative endeavor - YHWH created for 6 days then rested from his work on the seventh. Most Rabbinical's teach the definition of Melacha taken from http://www.chabad.org/:
The Hebrew language has two words for "work"--avodah and melachah. Avodah is a general term meaning work, while melachah has a very precise halachic meaning. On Shabbat, melachah is prohibited. Our Sages explain that melachah refers to the activities which were necessary for construction of the Mishkan, the traveling sanctuary which the Jews took with them throughout their desert wanderings.
Neither definition, in my opinion, would include electricity as Melacha. So, who decided turning on and off your lights was melacha? And, in any case, do you believe a goy who was hired to turn on or off your lights would be considered "your" servant?
Exodus Chapter 20
8 Remember the sabbath day, to keep it holy.
9 Six days shalt thou labour, and do all thy work (Melacha);
10 but the seventh day is a sabbath unto YHWH thy God, in it thou shalt not do any manner of work (Melacha), thou, nor thy son, nor thy daughter, nor thy man-servant, nor thy maid-servant, nor thy cattle, nor thy stranger that is within thy gates;
11 for in six days YHWH made heaven and earth, the sea, and all that in them is, and rested on the seventh day; wherefore YHWH blessed the sabbath day, and hallowed it.

Exodus Chapter 23
12 Six days thou shalt do thy work, but on the seventh day thou shalt rest; that thine ox and thine ass may have rest, and the son of thy handmaid, and the stranger, may be refreshed.

Deuteronomy Chapter 5
12 Observe the sabbath day, to keep it holy, as YHWH thy God commanded thee.
13 Six days shalt thou labour, and do all thy work;
14 but the seventh day is a sabbath unto YHWH thy God, in it thou shalt not do any manner of work, thou, nor thy son, nor thy daughter, nor thy man-servant, nor thy maid-servant, nor thine ox, nor thine ass, nor any of thy cattle, nor thy stranger that is within thy gates; that thy man-servant and thy maid-servant may rest as well as thou.
15 And thou shalt remember that thou was a servant in the land of Egypt, and YHWH thy God brought thee out thence by a mighty hand and by an outstretched arm; therefore YHWH thy God commanded thee to keep the sabbath day.

Legendary literature contains many instances in which the Shabbat goy was replaced by a Golem. The latest story in which the Shabbat goy plays a r'le is that of K. L. Silman Franco, in Hebrew, in "Aḥiasaf," ). Maxim Gorki, the Russian novelist, was once employed as a Shabbat goy by the Jewish colonists in the governments of Kherson and Yekaterinoslav.

Bibliography: Jacobs, in Jewish Year Book, ), p. 291.