Ok - I know that you have done other stuff with dates and datagridview from your earlier posts.
So now you have a list of months by name rather than the datepicker control you were using before...
You will need to make use of the static methods on the DateTime class to work out the month number and then days in that month. For example:
int MonthNumber = DateTime.ParseExact("March", "MMMM", CultureInfo.CurrentCulture).Month;
int daysInMonth = DateTime.DaysInMonth(2013, MonthNumber);
Then you can populate your gridview as you have been doing.
The only thing to be wary of is February - if you want to cater for Leap Years you will need to adjust the year used above.