This is the simplest way but not performance efficient. as this query will not make use of any indexes defined on the DateColumn.
SELECT *
FROM Table_Name
WHERE MONTH(DateColumn) = 12 --<-- Month December
AND YEAR(DateColumn) = 2013 --<-- Year 2013
A better approach will be something like ...
For example if you want all the records in JUNE 2013 you could do something like .....
SELECT *
FROM DateColumn >= '20130601'
AND DateColumn <= '20130630'