The simplest formula would just be
Month([userSelectedDate])
This would return a number for the month and you could make your decisions based on that number.
If you must have the text name of the month, use
Case(Month ([userSelectedDate]), 1,"January",2,"February",3,"March",4,"April",5,"May",6,"June",7,"July",8,"August",9,"September",10,"October",11,"November",12,"December"))
Hope this helps,
~Rob