For individuals

A traditional 3 letter monogram is the person's first name initial on the left, the last name initial in the middle & larger, and the middle name initial on the right.  If the monogram is for a married woman,  it has been traditional to substitute her maiden name initial for her middle name initial on the right. In this case, her first name initial  is on the left, her last name initial is in the middle & larger, and her  maiden name initial is on the right. Individuals may also choose a two letter monogram, first and last initials.

For married couples with the same last name

In recent years couples have most often been choosing a "duogram" or joined monogram.  The wife's first name initial is on the left, the couples' last name initial in the middle & larger, and the husband's first name initial on the right. 

For couples with different last names or hyphenated last names

Options include a 2 letter monogram using the initials of  both last names or both first names with the woman's on the left. Prince William and Catherine used an intertwining WC for their monogram.  It has been a tradition for hundreds of year for royalty to use each of the couples' first names intertwining. It is also an option to have a custom 4 letter monogram designed with both  of the couple's first and last initials.

Most importantly

Most importantly, your mongram should represent what is most meaningful to you. If you have a monogram whose acronym has other meaning as well, it is completely fine to switch the letters. For instance, we had a couple whose duogram would have been "diy" (do it yourself) and they chose to switch it to "yid" but also considered a two letter. In the end, it's your choice!