The Shulhan Aruch (244:5) rules that it is permissible to hire a Non-Jew as a personal tailor or secretary, on a yearly basis. Even though the Non-Jew might make the suit or write the letters on Shabbat, it is still permissible, since the Jew doesn't care when he does it. There is no benefit to the Jew if the employee does the work on Shabbat; he is paying him an annual retainer. This leniency is based on the opinion of the Rambam.
The Shulhan Aruch then brings down a "yesh omrim", the Raavad, prohibiting such an arrangement. The Raavad argues that if the Non-Jew performs the task on Shabbat, the Jew benefits the availability of the employee on Sunday to carry out new tasks. Nevertheless, the Shulhan Aruch himself holds that, in principle, it is permitted.
However, this leniency only applies to cases in which the Non-Jew is performing work on his own premises. A Non-Jew is never allowed to do work in the Jew's house. Therefore, the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) rules that maids are not allowed to violate the Shabbat in the home of their Jewish employer. Even if they would be paid on a per-task basis, which is not the usual arrangement, it is still prohibited because of M’arit Ayin .
There are some poskim that even prohibit work done by the maid for her own personal benefit, e.g. doing her own laundry. However, clearly, a maid is not allowed to do the laundry of her Jewish employer in their home on Shabbat, even if she is only doing it then to clear her schedule.
A maid is allowed to do work in a prohibited way that could have been performed by in a permissible fashion by the Jew. For example, she is allowed to wash dishes with hot water, since the Jew could also have washed them with cold water.
Those that employ help in the house must be very careful to know the parameters of what work is permissible for them to do and what is forbidden.
SUMMARY
It is permitted to hire a Non-Jewish tailor or secretary on an annual basis to perform work on demand in the Non-Jew’s premises.
It is never permitted for a Non-Jewish maid to do prohibited work in the home of the Jew on Shabbat.
A Non-Jewish maid is allowed to wash dishes with hot water on Shabbat in the home of a Jew.
