When does Ramadan start?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

If you mean by your question when it is possible to prove the beginning of Ramadan, then, religiously, the evidence of the beginning of the month of Ramadan, is by the sighting of the moon (crescent), or considering the month of Sha'baan 30 days. Allaah Says (which means): {So whoever sights [the new moon of] the month [of Ramadan], let him fast it}[Quran 2:185]. Moreover, the Prophet said: "Fast upon sighting it (after you have seen the new crescent) and end the fast (at the end of the month) when you sight it. If it is hidden from you (due to clouds), then complete Sha'baan thirty days." [Al-Bukhari]

However, if you mean by your question when does Ramadan start this year [according to A.D. year], then it starts in October [probably on the 4th] but what decides the matter is the sighting of the moon or completing Sha'baan thirty days. 

Allaah Knows best.