Fasting during the month of Muharram is very good, as after Ramadan, the fasts of this month are better than the rest.
(Saheeh Muslim)

Plan for keeping a fast on tenth (10th) of Muharram (Ashura) for keeping fast on this day is very good.
(Saheeh Bukhari, Saheeh Muslim)

And also for the reason that the Jews celebrate Eid on this day so by keeping fast on this day demonstrate dissidence and opposition to them.
(Saheeh Muslim)

The Jews, not only celebrate Eid on the day of Ashura, but also keep fast on this day. Therefore as an attempt to demonstrate further dissidence and opposition to them, along with 10th also keep a fast on 9th of Muharram.
(Saheeh Muslim)

By keeping fast on Ashura, all the sins of the preceding year are forgiven.
(Saheeh Muslim)

Note: Besides the above-mentioned events, whatever is done during the month of Muharram is without any evidence or proof. It may be first or tenth of Muharram or the events taking place during the Ashura or the whole month of Muharram. Even there is no narration in support of serving food on tenth of Muharram. The holy prophet, SallAllah-u-Alaihi-wa-Sallam, by declaring Muharram as the month of Allah, has pointed towards its sacredness and sanctity. As such all the events related to joy and happiness can be celebrated during the month of Muharram.
(Saheeh Muslim)

Muharram is a month of sanctity and reverence, and there ought to be no war in this month.