How to extract month and year from date, then use them in a relationship

Create a new formula text field. Here is the code below 


Case(Month(ToDate([Date Created])),
1,"January",
2,"February",
3,"March",
4,"April",
5,"May",
6,"June",
7,"July",
8,"August",
9,"September",
10,"October",
11,"November",
12,"December",
"")

This will create the month based on the date created. I think the issue you are having is that date created is a date/time field and not a date field. You need to do a typeconversion first using ToDate.