fasting begins upon sighting the new moon after the ending of the month of sha'ban (on the lunar calendar). allah says:

 
"so everyone of you who is present (at his home) during that month should spend it in fasting."
 

[noble quran 2:185]

however, it is not incumbent on each person to sight the new moon. if a trustworthy muslim testifies that he has sighted it then everyone must observe fasting. abu hurairah says: "a bedouin [dweller of the desert] came to the prophet (peace be upon him) and reported; 'o prophet i have seen the new moon of ramadan.' so the prophet (peace be upon him) asked the man; 'do you bear witness that {laa elaha illa allah} there is no deity worthy of worship throughout the creation - only allah, the creator is worthy of worship?' the man said; 'i do'. then the prophet (peace be upon him) said; 'do you testify that muhammad is the messenger of allah?' then man said; "yes." so the prophet (peace be upon him) asked bilal to announce to the people to being their fast the next day."

ibn 'umar also confirmed the practice of sighting the new moon in his report: "the people were seeking the new moon. having sighted it myself, i reported it to the prophet (peace be upon him). he began his fast and ordered the people to being theirs too."

he who sights the new moon of ramadan must inform those in authority in the muslim government or community. once the muslim government announces the beginning of ramadan, upon sighting the new moon, it becomes binding on the rest of the muslims to being their fasting.

it should be kept in mind, however, that astronomical calculations must be ruled out from shari'ah and must not be relied on for sighting the moon, as the prophet (peace be upon him) has ruled that muslims must begin their fast upon seeing the new moon, not upon calculating the month astronomically. it is only when it becomes hard to see the new moon, due to weather conditions, then muslims may complete the month of sha'ban, which precedes the month of ramadan, as thirty days.

(the lunar month is either 29 or 30 days according to the sighting of the new moon. it is never more or less in number.)