Google decided to create a standalone Photos service that didn't need to run inside of Google+. Unfortunately, some of the sharing issues present in Google+ Photos also made their way to the Web version of the new service. Read on to learn about both sharing methods, and which one is right for you.
Official sharing feature
Using the share icon in the top right-hand corner of the Web UI will allow you to grab a shareable link. If you are viewing an album, the link will point to the entire album (which you can continue adding photos to). The main perk to using this method is that it will be easy for a viewer with a Google Photos account to add the images to their own collection. If you change your mind about sharing specific content, you can delete the link. To do so: open the left-hand menu, head to Shared Links, click Delete and confirm your choice.
Unofficial sharing method
This method is super fast and simple: just right-click on a photo and use the Copy image URL option. This URL will not appear in your Shared Links menu, and it will continue pointing to content until you remove that content from Google Photos. Because you're only linking to one image at a time, you won't need to worry about accidentally adding the wrong photos to an album you previously shared.
The new Photos service isn't packing all of the features that Google+ offered to users, but hopefully those left behind will find the way to their new home. For more information on the new service, check out Matt Elliott's Getting started with Google Photos.