Q: I've heard that it's not permissible to fast on Friday by itself without adding either a day before or after to it. If this is the case what do we do this year if Arafat falls on a Friday and someone wants to only fast the day of Arafat?
It is true that one should avoid fasting on Friday by itself. There are hadith that indicate that the practice should be avoided. However, if one is accustomed to fasting on a certain day or a special day such as 'Arafat or 'Ashura were to fall on a Friday then one could fast that day by itself because they would be intending to fast on the special day and not Friday per say.
That being said, the first ten days of Dhul Hijjah are the best days of the year and one should strive to do as many good deeds as possible during that time. This could include fasting as many of the first nine days as possible (the tenth is the Day of Eid wherein it is impermissible to fast). This especially includes the day of Arafat about which the Prophet (pbuh) said that fasting on it expiates the sins of the previous year and the coming year.
For more on fasting during the first days of Dhul Hijjah see here.
For more on the ruling of singling out Friday for fasting see here.
For more on observing a recommended fast on Friday see here.