Sheikh Sulaymân al-Tuwayjirî
It is preferred to fast the first nine days of Dhû al-Hijjah, the best day of which is the day of `Arafah.
It is preferred to fast the day of `Ashurâ’ (the tenth day of the month Muharrum) alomg with one day before it or one day after it or both.
It is also preferred to fast three days out of every month, most emphatically preferred on the 13th, 14th, and 15th of the month.
Also, fasting on Mondays and Thursdays is recommended.
The best fast of all is to fast every second day. This is the fast of Prophet Dâwûd (peace be upon him).
It is recommended to fast at least 6 days in the month of Shawwâl, after Ramadan. This should be accomplished only after fasting the full month of Ramadan, or making up any days missed in Ramadan.
Allah knows best.
Source: Islam Today