Assalamu alaikum, per global moon sighting (in Chile per CrescentWatch and moonsighting.com), the month of Shawwal began on August 8, 2013. for those who strictly follow a sighting within their local area, Shawwal began on August 9th, 2013, at least in North America.
Per the Ummul Qura calendar, Shawwal is calculated to have begun on August 8, 2013, this also falls in line with sighting reports coming out of Saudi Arabia which were demed by CrescentWatch and moonsighting.com to have been erroneous.
Given the above, the 29th day of Shawwal and hence the next time to go out and look for the hilal of Dhul Qi’dah will be on September 5th for those following global sighting and September 6th, for those following a local sighting in North America. Thus the first day of Dhul Qi’dah will either be on the 6th or 7th for those following a global sighting, or the 7th/8th for those following local sighting in North America.
The calculated date per the Ummul Qura calendar for the beginning of Dhul Qi’dah is on September 7th. I’m not sure if the Saudi govnerment makes moon sighting announcements for any other months besides Ramadan, Shawwal, and Dhul Hijja, if they do and they can be found online, let me know.