Per the Fiqh Council of North America (FCNA), the first night of Taraweeh will be on Friday, June 27th and the first day of Ramadan will be on Saturday, June 28th. Isha will start at 10:15 p.m.

Aashura is on the 10th day of Muharram, the first Islamic month. It is highly recommended to fast on the 9th and 10th (or the 10th or 11th) of this month. Prior to the fasting of Ramadan becoming necessary, Aashura was an obligatory fast for the Muslims. This day marks a great day in which Allah (swt) saved Musa (Moses) and the Israelites from the persecution of the Pharaoh.

According to Sunni Muslim tradition, Ibn Abbas narrates that Muhammad came to Medina and saw the Jews fasting on the tenth day of Muharram. He asked, “What is this?” They said, “This is a good day, this is the day when Allah saved the Children of Israel from their enemy and Musa (Moses) fasted on this day.” So he fasted on this day and told the people to fast." Read more about this day and the immense merits of fasting on this day.

According to the Fiqh Council of North America, the first of Muharram 1435H will be this Monday, Nov. 4, 2013. Therefore, the Day of Ashura will be on Wednesday, Nov. 13, 2013.

That means it is best to fast on either Tuesday (12th) and Wednesday (13th) or Wednesday (13th) and Thursday (14th). 
A humble reminder for us to plan our schedules next week so we can take advantage of a the manifold blessings from a fast on these two days.