Not fasting when in doubt: Fasting is based on the moon. Consequently the ‎Prophet [sallallaahu alaihi wa sallam] made special ‎arrangements to sight it. If the moon was sighted He ‎‎[sallallaahu alaihi wa sallam] would fast and If the moon could not be sighted due to clouds the Prophet [sallallaahu alaihi wa sallam] would not begin Ramadhaan but would complete 30 days of Shabaan.

It is narrated from Umm ul Momineen Syeda Aisha:

“He [sallallaahu alaihi wa sallam] began fasting after sighting the moon of Ramadhaan and if it was cloudy he would count 30 days (of Shabaan) and then fast.”

(Abu Dawud)

Fasting when the moon cannot be sighted:

For the ease and comfort of His ummah He [sallallaahu alaihi wa sallam] taught the same; fast (fasting) when the moon is sighted and if the moon cannot be sighted due to clouds etc do not fast on the day of doubt but complete thirty days of Shabaan and then begin Ramadhaan. He ordered the same for Eid.

Syeduna Abdullah bin Umar narrates that the Prophet [sallallaahu alaihi wa sallam] said:

“So do not fast (fasting) until you see the moon and do not break the fast until you see the moon. If it is cloudy then complete thirty days.”

(Abu Dawud)

It is from Syeduna Abdullah ibn Abbaas that the Prophet [sallallaahu alaihi wa sallam] said:

“Verily Allah Taala has given us time until the sighting of the moon and verily if it is cloudy then complete the term of thirty days.”

(Muslim, book of Siyaam)