The following is for Alexandria v.5.4.3. Below are instructions for v5.44 and v5.5x
Alexandria will calculate a grade based on a graduation year. This calculation is based on the date in your preferences.
To check this date, go to the Edit menu and select Preferences. From the pull down menu in the top right hand corner change Administration to Library Information and select the School tab. You should see the "Late date of school is" field as seen below:

In order to promote your students, the date in this field should be prior to the date in your date/time control panel. Once this date has passed, the patron record will automatically reflect changes in the level field.
The following is for Alexandria v.5.4.4
In the v.5.4.4 series, these preferences are located under Library Information > Global > Library Information Tab (screenshot below)

The following is for Alexandria v.5.5x
With Alexandria 5.5 and higher, use of Alexandria's Patron Grade Table will making promoting patrons an easier process. You can locate the Patron Grade Table by going to the following:
Edit > Preferences > Patron Management > Global > Grade tab (sometimes called Levels)

Here you can change, add, or remove grade codes and their descriptions. To advance all patrons grade levels, change the Last Day of School setting from the last day of school this year to the last day of school next year. For example if the 2008 school year were ending, you would update the date to the last day of school in 2009.
If this does not automatically upgrade your patron grades, you have the option of clicking the Advance Grades button which will promote all patrons one grade level. Please note that after clicking this button, you can not reverse the advancement, so be sure to only click this once. It is a good idea to have a backup or archive of your database before advancing patron grades in case you wish to revert back to previous data.