Praise be to Allah.
If we do not know whether the month of Dhu’l-Hijjah is complete (30 days) or imcomplete (29 days), and no one tells us when the new moon of Muharram was sighted, then we should follow the basic principle, which is that the month should be completed as thirty days. So Dhu’l-Hijjah is counted as being 30 days long, then we calculate the date of Ashura on that basis.
If a Muslim wants to be sure that he has fasted on the right day, he should fast two consecutive days at Ashura. So he should calculate when Ashura will be if Dhu’l-Hijjah is twenty-nine days and if it is thirty days, and fast these two days. Thus he will be definite that he has fasted Ashura, and in this case he will have fasted either the ninth and tenth, or the tenth and eleventh, both of which are good. If he wants to be sure of fasting Taasoo’ah (the ninth of Muharram) as well, then he should fast the two days we have spoken of above and the day immediately before them as well. Then he will have fasted the ninth, tenth and eleventh, or the eighth, ninth and tenth. In either case he will have fasted the ninth and tenth for sure.
If someone were to say “My work and other circumstances only allow me to fast one day, so which is the best day for me to fast?” we say to him:
Count Dhu’l-Hijjah as being thirty days and work out the tenth day (of Muharram), then fast on that day.
This is a summary of what I heard our shaykh, ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him), say when I asked him about this matter.
If we receive news from a trustworthy Muslim that he has seen the new moon of Muharram, we should act in accordance with that. Fasting at any time in Muharram is Sunnah, because the Prophet (peace and blessings of Allah be upon him) said: “The best fasting after the month of Ramadan is fasting in the month of Muharram.” (Narrated by Muslim, 1163)
And Allah knows best.