A friend of mine shared an album with me on Google Plus. I'd like to add this album to my albums so that I can see it in the Photos section. How to do it? There is no button for this action, does that mean that I need to download the photos and re-upload them to my G+ profile? That would be a bit impractical as I would need to re-tag everyone etc.
As far as I know, Google+ Photos is not intended to manage photos owned by another user, so there is no other way than getting the photos someway and then add them through any of the photo management services from Google:
It is better to use Picasa Web Albums instead, if you are interested. You don't need to download and upload all photos. However, there isn't anything matching exactly with your request in Google+ at the moment.
The another way is using Google Drive to store your photos in the cloud, and the non-Google alternatives are Dropbox, Box and iCloud Drive.
Also you can use the new photo services from Google, like Google Photos, Google+ Photos, and Picasa. And don't forget services other than Google, like iCloud Photo Library. You can easily add photos from Google to iCloud, or the better way is to ask the person who shared the picture to share them with you on iCloud Photo Library, if both have iOS or Mac devices (iOS 8+, OS X 10.10.3+).