"The blessed month of Ramadhan has passed us by but we should beware from becoming lax towards the ibaadaat (worship) we attempted to excel in during this month. Try to maintain the extra rakaats, reading more Quran and allocate a portion of the night for prayer. May Allah(SWT) grant us steadfastness and tawfique.
It is also recommended to fast six days in this month - Rasoolillah (SAW) said, "Whoever fasted the full month of Ramadan and then follows it with the six fasts of Shawwal, is like a person who has fasted the full year." (Muslim) "

From Sunnipath.com:
Question:
Can one make up the intention of fasting for shawwal and the missed fasts due to womens' precious time as a double count? or does one have to make up the missed fasts and then fast for shawwal?
Answer:
In the Name of Allah, Most Merciful & Compassionate
From a previous question answered by Sidi Faraz Rabbani:
If one fasts any 6 days (even makeups) in Shawwal, one gets the reward of performing the sunna of fasting six days of Shawwal
Please also see the following link in answer to your question:
RE: Fasting 6 Days of Shawwal after Ramadan: 'Like Fasting the Entire Year'
http://www.sunnipath.com/resources/Questions/qa00000322.aspx