The Month of Shawwal starts when the month of Ramadan finishes. It is recommended to fast 6 days in Shawwal but not obligatory. Abu Ayyoob (may Allah be pleased with him) reported that the Messenger of Allah (peace and blessings of Allah be upon him) said:
“Whoever fasts Ramadaan and follows it with six days of Shawwaal, it will be as if he fasted for a lifetime.” (Narrated by Muslim, Abu Dawood, al-Tirmidhi, al-Nisaa’i and Ibn Maajah).
The Prophet (peace and blessings of Allah be upon him) explained this when he said:
“Whoever fasts for six days after (Eid) al-Fitr has completed the year: (whoever does a good deed (hasanah) will have ten hasanah like it).”
According to another report:
“Allah has made for each hasanah ten like it, so a month is like fasting ten months, and fasting six days completes the year.” (al-Nisaa’i and Ibn Maajah. See also Saheeh al-Targheeb wa’l-Tarheeb, 1/421).
It was also narrated by Ibn Khuzaymah with the wording:
“Fasting for the month of Ramadan brings the reward of ten like it, and fasting for six days brings the reward of two months, and that is the fasting of the whole year."
You do not have to fast all 6 fasts consecutively. What is needed is that the total number of fast you make in shawwal should add up to 6.
However whilst fasting in shawal (or other months ) you should not single out Friday for performing a naafil (voluntary) fast
Abu Hurayrah (may Allaah be pleased with him) said: I heard the Prophet (peace and blessings of Allaah be upon him) say: “No one of you should fast on Friday, unless he fasts (a day) before it or after it.” (Al-Bukhaari (1985) and Muslim (1144) )
Narrated from Juwayriyah bint al-Haarith (may Allaah be pleased with her), that the Prophet (peace and blessings of Allaah be upon him) entered upon her on a Friday and she was fasting. He said; “Did you fast yesterday?” She said, “No.” He said: “Do you intend to fast tomorrow?” She said: “No.” He said: “Then break your fast.” (al-Bukhaari (1986) )
Also Allah says: “Then when the (Jumu‘ah) Salaah (prayer) is ended, you may disperse through the land, and seek the Bounty of Allah (by working), and remember Allah much” [al-Jumu’ah 62:10].
Sisters in particular should note that scholars have said that fasting six days of Shawwaal is dependent upon having completed the Ramadan fast, which is indicated by the words of the Prophet (peace and blessings of Allah be upon him): “Whoever fasts Ramadan then follows it with six days of Shawwaal, it will be as if he fasted a lifetime.” Narrated by Muslim, 1164.
The conjunction thumma (then) indicates that this must be done in this order. This indicates that the fast of Ramadan must be completed first (by observing the Ramadan fast and making up any missed fasts), then after that one may fast the six days of Shawwaal, so as to attain the reward mentioned in the hadeeth.
Scholars also said it is disliked (makrooh) to single out fasting on Saturday for fasting
Narrated by al-Tirmidhi (744), Abu Dawood (2421) and Ibn Maajah (1726) from ‘Abd-Allah ibn Busr, from his sister, that the Messenger of Allah (peace and blessings of Allah be upon him) said: “Do not fast on Saturdays apart from days when you are obliged to fast. If any one of you cannot find anything other than grape stalks or the twigs of a tree, let him chew it (to make sure that he is not fasting).” Classed as saheeh by al-Albaani in al-Irwa’ (960). Abu ‘Eesa al-Tirmidhi said: This is a hasan hadeeth
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
It should be noted that different scenarios may apply with regard to fasting on a Saturday.
1 – It may be obligatory, such as observing a Ramadan fast during Ramadan or making it up later on, or observing a fast as expiation (kafaarah), or instead of offering a sacrifice when performing Hajj tamattu’, and so on. There is nothing wrong with that so long as he does not single it out deliberately thinking that there is some virtue in that.
2 – If he fasts on the Friday before, there is nothing wrong with it, because the Prophet (peace and blessings of Allah be upon him) said to one of the Mothers of the Believers who was fasting on a Friday: “Did you fast yesterday?” She said: “No.” He said: “Are you going to fast tomorrow?” She said, “No.” He said: “Then break your fast.” The words, “Are you going to fast tomorrow?” indicate that it is permissible to fast Saturday along with Friday.
3 – If it happens to be one of the days when it is prescribed to fast, such as Ayyaam al-Beed (the 13th, 14th and 15th of each hijri month), ‘Arafah, ‘Ashoora’, six days of Shawwaal for one who has fasted Ramadan, and the ninth of Dhu’l-Hijjah. There is nothing wrong with that, because he is not fasting because it is Saturday, rather it is because it is one of the days when it is prescribed to fast.
4 – When it happens to be a day when he habitually fasts, such as a person whose habit is to fast alternate days, and the day that he fasts happens to be a Saturday, then there is nothing wrong with it, as the Prophet (peace and blessings of Allah be upon him) said when he forbade fasting one or two days before Ramadan begins: “except a man who (habitually) observes a fast, in which case let him fast.” This is similar.
5 – If he singles it out to observe a voluntary fast for one day only. This is what is forbidden, if the hadeeth forbidding it is proven to be saheeh.
End quote from Majmoo’ Fataawa wa Rasaa’il al-Shaykh Ibn ‘Uthaymeen (20/57)
The Prophet Dawood used to fast for a whole year. What he would do was that he would fast one day and not fast the next day he would repeat this cycle for the whole year.
It is reported in al-Saheehayn from ‘Abd-Allah ibn ‘Amr (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “The best fasting is the fast of Dawood: he used to fast one day and not the next.”
Naturally if a Muslim performs the fast of Dawood he would be fasting some days on a Saturday and some day on a Friday and in this case it would be permissible. (note if a Muslim wanted to fast the fast of Dawood he/she can do so but they must fast the whole of Ramadan and in the months other than Ramadan they would be fasting one day on and one day of.
He replied: If a woman still owes days from Ramadan, then she should not fast the six days of Shawwaal until after she has made up what she owes, because the Prophet (peace and blessings of Allah be upon him) said: “Whoever fasts Ramadan then follows it with six days of Shawwaal…” Whoever still has days to make up from Ramadan has not fasted Ramadan, so she will not attain the reward of fasting the six days of Shawwaal until after she has finished making up the days she owes. If we assume that this making up missed fasts lasts throughout Shawwaal, such as if a woman was bleeding following childbirth and did not fast at all in Ramadan, then she started to make up her missed fasts in Shawaal and did not finish that until Dhu’l-Qa’dah began, then she may fast the six days, and she will have the reward of one who fasted them in Shawwaal, because she delayed it for a necessary reason, so she will have the reward.
Majmoo’ al-Fataawa, 20/19
Another benefit of fasting the naawafil fasts is that they may help compensate for any shortcomings in our fasts. The Prophet peace be upon him said.
“The first thing for which people will be brought to account on the Day of Resurrection will be their salaah (prayer). Our Lord, may He be glorified and exalted, will say to His angels – although He knows best – ‘Look at the salaah of My slave, whether it is complete or incomplete.’ If it is perfect, it will be recorded as perfect, and if something is lacking, He will say, ‘Look and see whether My slave did any voluntary (naafil) prayers.’ If he did some voluntary prayers, [Allah] will say, Complete the obligatory actions of My slave from his voluntary actions.’ Then all his actions will be dealt with in a similar manner.” (Narrated by Abu Dawood)