Select the Announcements tool from the Tool Menu of your site.

Drag and drop with your mouse or use keyboard U and D keys to reorder an announcement.

There are five options that allow you to auto-sort the Announcements:

1. Sort by subject - orders the announcements in alphabetical order according to the subject line
2. Sort by author - orders the announcements in alphabetical order according to the person who created the announcement
3. Sort by beginning date - orders the announcements based on first date of display
4. Sort by ending date - orders the announcements based on last date of display
5. Sort by modified date - orders the announcements in order based the creation (or most recent modification) date

When you click one of the five options in the header row, an arrow icon appears beside it. If the arrow icon points upwards, it indicates that the list is sorted smallest to largest. If the arrow icon is pointing downwards, it indicates or largest to smallest. 

In the above demonstration, the announcements are sorted by modified date, with the oldest at the top and the most recent at the bottom. Click the arrow icon in the Sort by modified date cell again to change the sorting to instead display most recent at the top and oldest at the bottom.