Ashura is the 10th of Muharram, the first month of the Islamic calendar.
According to moonsighting reports (see: moonsighting.com), it falls on september 10th 2019.
It is recommended, in the Sunni and Zaydi Shi`i schools, to fast the day. There are numerous sahih hadiths about its fasting, some of them mentioning that it was an obligatory fast in the days before fasting Ramadan became obligatory.
وقال أحمد بن عيسى بن زيد بن علي (عليهم السلام) في أماليه: صوم الأيام البيض، ورجب وشعبان، والإثنين والخميس حسن جميل، وجاء فيه فضل كثير، وكذلك يوم عاشوراء
According to one sahih hadith, the Prophet Muhammad later expressed his wish to also fast on the 9th of Muharram (the day before Ashura), but he died before that could happen.
وعن أبي عبد الله عليه السلام عن أبيه، أن عليا عليه السلام قال: صوموا العاشوراء التاسع والعاشر، فإنه يكفر ذنوب سنة (وسائل الشيعة)
A hadith of disputed reliability says that the Prophet recommended, along with the fast of Ashura, fasting either the day before or the day after.
One version (with a weak isnad) indicates all three days.
أفضلُ الصيامِ بعدَ رمضانَ شهرُ اللهِ المحرَّمُ (رواه مسلم)
The dominant view among Twelver Shi`ah is that it is not recommended to fast Ashura. One narration in the Twelver hadith books suggests that it is a fast that was abandoned after Ramadan became obligatory.
The killing of the Prophet's grandson was a tragedy, and is a source of grief for Sunnis and Shi`ah. If you fast Ashura, it should definitely not be with the intention of celebrating Imam Husayn's murder.