Picasa used to upload folders from a computer to albums with the same name, even in batch, and (optional) sync computer folders with Google Photos. The actual Photos team however did not find it necessary to implement such option. Adding photos to albums in Google Photos is now always a manual action.
For photos that are already uploaded to Google Photos, you can:
Select (multiple) photos anywhere in Google Photos, and add them to an album via the + icon (Add to).
In the web app you are offered the choice between Album and Shared Album. I always select Album: you can share later, and it offers recently used albums on top. When you click on Album, you are offered the choice between New album or an existing one.
On Android it only offers Album, but tapping on it creates a new album immediately.
Tip: on a computer you can find an existing album by using the Find function (Ctrl+F) of the browser.
Or start from the album and use the "Add photos" icon (icon with a small +)
This brings you to the timeline where photos that are already in the album are selected.
Warning: deselecting will remove these photos from the album!
Tip: you can also "Select from computer" or use the search box to find photos.
When you upload photos manually from a computer to Google Photos, you get a pop-up asking whether you want to add the uploaded photos to an album. When you missed that option, you still find newly added photos on top in Recently added.
Warning: Photos/videos that were already uploaded will NOT be uploaded again, and NOT added to the album. Therefore I recommend the method described hereafter, to upload directly to an album.
Upload directly to the album, either by drag & drop into the open album or by using the "Add photos" icon in the album. When using this method, ALL photos should be added to the album, even when you try to upload duplicates.
Tip: You can use this method also when the photos are already uploaded.
When your photos are already uploaded, for example by using Backup, you can still:
Go to Collections > on this device (Android only) or anywhere in the Google Photos app
Select photos you want to add to an album
Tap the + icon > Album or select an existing album
Warning: when you (accidentally) touch an album the photos are added immediately without confirmation. You will have to find them there, add to the correct album, and remove from or delete the wrong album.
You can also add photos to an album when they are not yet uploaded to Google Photos. That should also upload them to the Google Photos timeline.
Warning: When uploading manually (3-dots > Back up now) or adding not-yet-uploaded photos to an album, the settings under "Backup" on the device are not valid:
For upload size it uses the setting in https://photos.google.com/settings
It may use mobile data, regardless the setting in Backup and sync.
Some users (like me) want ALL photos in albums. Former Picasa users already had obligatory ALL photos in Picasaweb albums when Google Photos was introduced in 2015. They could rather easily continue to add all newly uploaded photos to albums. It's more difficult when you start using Google Photos with a big collection.
The info of a photo shows all albums to which the photo was added, but there is no easy way to find which photos are not in any album. See Photos not in any album
Some recommend to hide the photos by moving them to "Archive". That is a not intended use of the archive (intended to hide "clutter"), and may have unwanted effects, like photos not being shared by partner sharing, not added to live albums or not used in Memories. I don't recommend that method, also because archiving from within an album is not implemented: you will have to select them again somewhere else, for example in a search result by searching with the complete album title.
What you can do:
Adding photos to albums can often be done in batches, based on events, dates, etc. Staring from an album to complete it is much more difficult, if possible.
You can also add photos to albums starting from folders on a computer or on mobile devices (see higher).
You can systematically add new photos to albums, and add the backlog starting from the top (newest), note the date on which you stopped of the where you stopped and continue from there next time.
Removing photos from albums is more efficient when you can remove selected photos in batch from the album. Trying to remove a photo you find somewhere else is very laborious: it's not easy to find a specific photo in an album. Deleting an album also removes that album from the info of all photos.
To avoid chaos on my main account I back up photos automatically from my phone to a second account, and add manually to albums in my main account what I want to keep. Stuff from WhatsApp etc. stays away from my main account unless I actively add it.