All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is recommendable to fast the whole of Allah's month Muharram, since it was reported by Muslim that the Prophet Muhammad said: "The best fasting after the month of Ramadan is Allah's month Muharram, and the best prayer after the obligatory one is the night prayer."
If it is difficult to fast the full month, the person can fast the day of ‘Ashoora’ (tenth of Muharram). There are three ways of fasting it:
1) The best is to fast the day before ‘Ashoora’ day, fast ‘Ashoora’ day, and fast one day after it.
2) Fasting the day before or the day after ‘Ashoora’, and fast the day of ‘Ashoora’.
3) Fasting the day of ‘Ashoora’ only.
Allah knows best.