Volume 3, Book 31, Number 205:
Narrated Muhammad bin ‘Abbas:
I asked Jabir (radiallaahu `anhu) “Did the Prophet (sallallaahu `alayhi wasallam) forbid fasting on Fridays?” He replied, “Yes.” (Other narrators added, “If he intends to fast only that day.”)
Volume 3, Book 31, Number 206:
Narrated Abu Huraira (radiallaahu `anhu):
I heard the Prophet (sallallaahu `alayhi wasallam) saying, “None of you should fast on Friday unless he fasts a day before or after it.”
Volume 3, Book 31, Number 207:
Narrated Abu Aiyub (radiallaahu `anhu) from Juwairiya bint Al-Harith (radiallaahu `anhaa):
The Prophet (sallallaahu `alayhi wasallam) visited her (Juwairiya) on a Friday and she was fasting. He asked her, “Did you fast yesterday?” She said, “No.” He said, “Do you intend to fast tomorrow?” She said, “No.” He said, “Then break your fast.” Through another series of narrators, Abu Aiyub (radiallaahu `anhu) is reported to have said, “He ordered her and she broke her fast.”
Ibn Qudaamah said:
It is makrooh to single out the day of Friday for fasting, unless that coincides with a fast which one usually observes, such as a person who fasts alternate days, and a day that he fasts coincides with Friday, or a person who has the habit of fasting on the first or last day of the month, or the middle day of the month.
(al-Mughni, vol. 3, p. 53)
Shaykh Ibn ‘Uthaymeen said:
As for Friday, it is not Sunnah to fast on this day, and it is makrooh to single it out for fasting.
(See al-Sharh al-Mumti’, vol. 6, p. 465)
Excluded from this prohibition is one who fasts the day before or after, or if it coincides with days that he habitually fasts, such as one who fasts al-Ayyaam al-Beed (the 13th, 14th and 15th of each hijri month), or who has the habit of fasting a specific day such as the Day of ‘Arafat, and it coincides with a Friday. From this it may be understood that it is permissible for a person who has vowed to fast on the day when so and so returns, for example, or the day when So and so recovers from sickness, to observe that fast if that day happens to be a Friday. (See Fath al-Baari by Ibn Hajar).
The same applies to one who has fasts to make up from Ramadaan. “It is permissible for a Muslim to fast on a Friday to make up a day from Ramadaan, even if he fasts the Friday on its own.” (Fatwa al-Lajnah al-Daa’imah, vol. 10, p. 347)
Similarly, if ‘Ashoora’ or Arafaat coincides with a Friday, he may fast, because his intention is to fast ‘Ashoora’ or ‘Arafaat, not to fast on a Friday. And Allaah is the Source of strength.
[Taken from IslamQA]