|(Credit: Screenshot by Jason Cipriani)|
To get the additional space, you need to download and install the latest beta build from the Dropbox forums. Make sure to create a backup of your Dropbox folder before installing the beta. The easiest way to do that is just to create an Archiver, or ZIP file, of the folder.
After installing the beta, you need to import photos to your Dropbox account. In order for the import to work, the photos will need to be on a camera, a smartphone, or a memory card. Once a compatible device is attached to your computer, Dropbox should automatically begin importing the photos to a new Camera Uploads folder in your Dropbox account. For every 500MB you upload, you will earn another 500MB of storage in your account, maxing out at the 4.5GB mark.
I have successfully earned the initial 500MB of extra space on my first import, and am currently waiting for the upload to finish on another 500MB, for yet more storage.