When you edit a photo in Picasa3, the desktop program, Picasa does not modify or replace the original photo, but rather, it records the edit in an "edit list" associated with that photo. Each time you perform another edit, that edit list is updated. If you close Picasa and come back another day, the edits are re-applied to the photo as it is displayed. This allows you to undo any edit at any time, even after closing and reopening Picasa.
Edits do not need to be saved
There is no need to save any of the edits you made in Picasa3. When you use Picasa to print, shop, upload (to Google Photos, Album Archive, Blogger), email using the Email button, export using the Export button, create collages, burn gift CDs, or otherwise use that photo in Picasa, all the edits you made are already applied to the photo. Because you did not "save" the edits, the original photo is not moved or modified in any way. There is no accumulation of JPEG compression artifacts if a series of edits is applied over time.
Reasons why you may want to save edits
If you want to use Picasa-edited photos to send email directly from an email provider, or to upload photos to non-Picasa websites (such as eBay, Ancestry.com, your personal website, etc.) or use those edited photos with other software (such as OpenOffice, LibreOffice, Word, Word Perfect or any other photo editing program), there are two ways to accomplish this:
Export (this saves a copy of the edited version to another location on your computer): Select all pictures that you want to export. Click File"/"Export Picture to Folder..." (or click the Export button). Click "Browse" to change the export location, if desired. You can type in a folder name in the "Name of exported folder" field. You can change the image size and quality, and add a watermark. After you click Export, all the selected pictures will be saved to another location on your computer. Use those exported photos with your other software or upload to your website. Your computer will now be storing both the original photo and the exported photo. You can safely delete the exported photo if you no longer need it after uploading or working with other software. Important!: Do not delete the original photo!
Save the edits (if you want the photos to reflect the changes in their original location): Click the "Save edited photos to disk" button (which will save all edits in that folder), or right-click on a photo and click Save, or click File > Save (which will save edits on an individual photo). Either of these actions will force Picasa to apply all edits, and it will replace the original file with the edited file. At the time when the edits are saved, the unedited original(s) will be automatically moved to a hidden folder (".picasaoriginals"). You can then use the "saved" version to upload to websites or use with other programs. The downside with saving edits is that now there will be two copies of those photos on your computer - the original (in a hidden folder) and the edited "saved" version. Having two copies will take up disk space on your computer. You can revert back to having just one version of the photo on your computer by undoing the save. The "Undo Save" button is available in the Picasa edit screen (or click File > Revert).