Fasting Six Days of Shawwaal

Abu Ayyoub reported that the Messenger of Allah, salla Allahu alaihi wa sallam said:
Whoever fasts the month of Ramadhan and then follows it by fasting six days during the month of Shawwal will be rewarded as if he had fasted the entire year
Fasting Six Days of Shawwaal - (The ClearSunnah.Blog) 
The reward of fasting the six days of Shawwaal, the manner of observing this voluntary fast 

Excerpts: Fasting the six (days) of Shawwaal is a recommended act of worship and not an obligation. It is not a must for him to fast immediately after ‘eed al-fitr, rather it is permissible to begin fasting after ‘eed by a day or (a number of) days. And (also) to fast them continuously or intermittently in the month of Shawwaal according to that which is easy for him."

And the issue is quite open in this matter, and it is not obligatory, rather it is a sunnah. These days can be anytime during the month of Shawwal except the first day because it is unlawful to fast the day of Eid. These days do not have to be at beginning of the month nor do they have to be consecutive.
Hence, Muslims should seize this opportunity and fast these six days to get Allah’s reward."He should not do the voluntary fast whilst he has a day or days to make up from Ramadhaan. Rather, he should begin by making up that which he has (outstanding) from Ramadhaan, then do the voluntary fast.

When to Fast the Six Days of Shawwaal

Must the six days of Shawwal be fasted directly after Eid day?
It is not necessary to observe this Sawm directly after `Eid-ul-Fitr.It is permissible to start observing it one or more days afterwards.The six days can be observed either consecutively or non-consecutively during the month of Shawwal, whichever is easier.This matter is open to choice, as this Sawm is Sunnah and not Faridah (obligatory act). May Allah grant us success.



 

Fasting Six Days of Shawwaal While Still Having Ramadan Fasts to Make Up

Voluntary Fasting

Voluntary Fasting in Islam - Salafi Publications 
Fasting in general and voluntary fasting in particular is a great worship of all time. Fasting is not restricted to Ramadhan, it is an act of worship that can be [and should be in some cases] performed at any time and at any place except when not recommended. Indeed, it is a worship that draws the believer closer to Allah and closer to perfection.

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Fasting Other Than Ramadan