Gemara

(Beraisa): Children do not learn new things on Shabbos, but they may do (even) the first review of what they learned. (We assume that new things are forbidden due to the Isur of taking wages for work done on Shabbos.)

Question: One may receive wages for work done on Shabbos, together with wages for work done during the week!

(Beraisa): If one hired a worker to guard (for the needs of Hekdesh) a child, a red heifer, or crops, he does not receive wages for Shabbos. Therefore, if they were lost (or became Tamei, on Shabbos), he is exempt;

If he was hired by the week, month, year or Shemitah cycle, he receives wages for Shabbos. Therefore, he must pay if they are lost.

Kesuvos 63a (Mishnah): If a woman rebels against her husband, we reduce her Kesuvah by seven Dinarim every week. If a man rebels against his wife, we add three Dinarim to her Kesuvah every week.

64a - Question (R. Chiya bar Yosef): When she rebels, we deduct from her Kesuvah corresponding to all seven days of the week, including Shabbos. When he rebels, why do we add to her Kesuvah only for six weekdays, but not for Shabbos?

Answer (Shmuel): When we subtract from her Kesuvah it does not look like wages, so we subtract even for Shabbos. Adding to her Kesuvah looks like wages, so we do not do so for Shabbos.

Rishonim

The Rif and Rosh (Shabbos 64b and 23:8) bring the Beraisa, and add 'he may not say 'give to me my wages for Shabbos', but he may say 'give to me my wages for the year' or 'for 10 days.'

Rambam (Hilchos Shabbos 6:25): If one hired a worker to guard a child or a Parah Adumah, he does not give to him wages for Shabbos. Therefore, he has no Acharayos (liability) for (mishaps that occurs on) Shabbos. If he was hired by the week, month, year or Shemitah cycle, he receives wages for Shabbos. Therefore, he has Acharayos for Shabbos. He may not say 'give to me my wages for Shabbos', but he may say 'give to me my wages for the year' or 'for 10 days.'

Rosh (Kesuvos 5:37): Even though Schar Shabbos is permitted through Havla'ah (being paid for Shabbos and Chol together), like it says in Bava Metzi'a (and Nedarim), regarding a rebel it is not Havla'ah. If he would cease to rebel in the middle of the week, we add only for the days of rebellion.

Hagahos Ashri: R. Baruch forbids hiring a Shali'ach Tzibur for Shabbos. R. Shmuel permits, since it is for the Mitzvah of prayer.

Beis Yosef (OC 306 DH v'Chosav): I do not understand R. Shmuel. Still, it is wages for Shabbos! Perhaps he means that the Isur is only mid'Rabanan, therefore we did not decree regarding Mitzvos.

Poskim

Shulchan Aruch (OC 306:4): If one hired a worker to guard crops or anything else, he does not give to him wages for Shabbos. Therefore, he has no Acharayos for Shabbos.

Mishnah Berurah (15): Even if the employer wants to pay, the worker may not accept it, unless it is given for a gift.

Mishnah Berurah (16): Schar Shabbos is forbidden mid'Rabanan. It is a decree lest one buy or sell.

Kaf ha'Chayim (29): The Ran (Shabbos 64b DH Lefichach) exempts for theft or loss. This connotes that he is liable for negligence.

Shulchan Aruch (ibid.): If he was hired by the week, month, year or Shemitah cycle, he receives wages for Shabbos. Therefore, he has Acharayos for Shabbos.

Mishnah Berurah (18): Even if no mishap occurred, if he did not guard on Shabbos, the employer can deduct for this.

Shulchan Aruch (ibid.): He may not say 'give to me my wages for Shabbos', but he may say 'give to me my wages for the week' or 'for the month' or 'for 10 days.'

Source (Gra DH v'Lo): This is from a Tosefta (Shabbos 17:28).

Rema: If he was hired by the month, for a certain amount per day, he is called a day laborer.

Bedek ha'Bayis (DH Kasuv): Shibolei ha'Leket says that if he says 'give to me this sum for the month, which is this amount per day', this is Schar Shabbos. He may say 'give to me my wages for the week' or 'for the month' or 'for 10 days.' The Poskim disagree.

Mishnah Berurah (20): Some permit, for presumably the employer will not retract in the middle, and he will pay for the entire month.

Magen Avraham (7): The Ran says that if he would cease working in the middle of the week, he would not be paid for the entire week, only for the days he worked. Therefore, he is (text of Dagul me'Revavah - not) a day laborer, and what he receives for Shabbos is Schar Shabbos. This is clear from the Gemara. The same applies to one who rents a room. It seems that the same applies to one who lends (to Nochrim) with Ribis. He must stipulate to collect Ribis for the entire week, even if the loan is paid in the middle. Even regarding a rebel, whom Chachamim fined to add to the Kesuvah every day, he does not add for Shabbos, for it would be Schar Shabbos. The same applies to all fines. To deduct from a debt every day is not Schar Shabbos. The Gemara in Kesuvos proves so.

Kaf ha'Chayim (33): Some say that it suffices to specify the interest for each week. If the borrower pays in the middle of the week, he owes for the entire week. We are not concerned if the lender pardons part of this.

Kaf ha'Chayim (34): If one is hired to guard before, during and after Shabbos and is paid for all together, it is permitted. However, if he deducts for when he did not guard, this is not Havla'ah. An innkeeper may take rental for Shabbos only if it includes for some time on Erev and Motza'ei Shabbos.

Shulchan Aruch (5): One may not hire a Shali'ach Tzibur for Shabbos. Some permit.

Mishnah Berurah (23): The same applies to hiring someone to blow the Shofar. Even those who permit hold that he will not be blessed through what he receives. One may not hire on Shabbos or Yom Tov itself.

Kaf ha'Chayim (37): We are lenient about all Mitzvos, including a Chacham who expounds, where people take wages for this.

Rema: If he was hired for a year or month, all permit.

Mishnah Berurah (24): This is when he is Shali'ach Tzibur also during the week, and he is paid b'Havla'ah. Acharonim are lenient even when he is hired only for Shabbos. To be stringent, one should not fix a wage, and later he may give a gift.

Kaf ha'Chayim (36): A midwife may accept Schar Shabbos, for it is Schar Mitzvah of Piku'ach Nefesh. One should not hire or and mention the wage on Shabbos. A doctor may take wages for Shabbos.