Using Picasa3
Open a photo
Type a caption in the "Make a Caption!" field below the picture
Captions added in Picasa3 are written to the metadata and are uploaded with the photo.
More tips for typing captions are here.
Using File Explorer in Windows 10
Find a photo in File Explorer (or select several photos)
Right-click the selection and click Properties
Click the Details tab
Type a caption in the Title field
Click OK
Captions added in File Explorer are written to the metadata and are uploaded with the photo.
Click a photo
Click the "i" (Info) icon
The Info panel opens up on the right side.
Type a caption
Captions added after uploading to Google Photos are NOT written to the metadata of the photo. The captions will be lost when you download from Google Photos. A way to preserve the captions was to download using File > Import from Google Photos in Picasa3 on the computer, but Google disabled that option in 2018. The only way left is by using Google Takeout but you need special software and skills. See this link.
Click a photo and click the "i" (Info) icon. The Caption is shown on top.
When the info panel is closed the caption is shown in the left lower corner.
Captions currently do not show when viewing a slideshow from the 3-dot menu.
Go to Album Archive: https://get.google.com/albumarchive
Click into an album
Click a photo
Click the "i" (info) icon
The Info panel opens up on the right side
The Info panel closes automatically when you leave the album and you need to click "i" again when viewing another album