Shawwal is the tenth month of the Islamic Lunar calendar. The first day of Shawwal is Eid al Fitr. After Eid, it is recommended for Muslims who are able to observe six additional days of fast.
It is believed that Abu Ayyoub reported that the Messenger of Allah (salla Allahu alaihi was sallam) said that whomever fasts the entire month of Ramdan and then fasts six days in the month of Shawwal will be rewarded as if he or she fasted the entire year (1). You take fast anytime during the month of Shawwal expect for Eid al Fitr. The days do not have to start at the beginning of the month, nor do they have to be consecutive. However, one must make any days prior to fasting the six days in Shawwal.
If you are able to, it is a good idea to take advantage of the reward of fasting six days in Shawwal.
(1) Ibn Shahid, “Fasting Six Days of Shawwal” From The Way of the Salaf us-Saalih. (September 29, 2008) retrieved September 28, 2008 from http://theclearsunnah.wordpress.com/2008/09/29/fasting-six-days-of-shawwal/.