Previously, if I uploaded photos from Picasa to PicasaWeb, I could specify them as Public but Unlisted. So you had to have the link to view them but no login was required.
I don't see that option now that Picasa uploads to Google+.
You should see a Visible to: title when you click through to the photo album you want to share via a private link.
Click that and you should see an overlay appear which includes an option to:
Copy and paste and send that link to whomever you want to have access to the album, while still keeping it away from public listing.
You can also click on the Options menu and Share album via link.
If you wanted to pass around an individual photo, just right-click and open the image itself into a new tab for its URL or "Copy the image URL" (or your browser equivalent to grabbing the URL of an image from the page).