You can format a date so that it only shows month and year, but leaves out the day. Select the date cell and open the Format Cells dialog, by pressing Ctrl - 1. Choose custom and then you can type mm-yyyy as the format to show just the month and year for your date.
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If you mean that you want to show the name of the month and the year in full format, then you can do it with the Format menu. Put the date into the cell you want and then put the cursor on that cell. Go to the Format menu and pick Cells. Under number you will see a list of different formats. It should already be on Date in the Category list on the Type side. You will be able to choose various formats for dates. You can also go to the bottom of Category list and pick Custom. That will allow you to do all sorts of date formats, even including showing the day of the week.
If you want to extract the number of a month from a date you can use the Month function. If your date is in cell C3 then the formula would be put into another cell and it would be:
=Month(C3)
To get the year you use the Year function:
=Year(C3)
To get the number of the day of the month, use the day function:
=Day(C3)