Remark: When you change the date in Google Photos, you do NOT change the date/time in the photo itself, but only in Google's database. As a result, the old date remains when you download the photos or look at them in other apps.
One by one in Google photos:
Go to photos.google.com
Click on the picture/video you want to change the date of
At the right-hand side at the top click on the "i" icon
In the pane at the right you can change the date
In bulk in Google Photos (new since May 24, 2016)
Go to photos.google.com
Select multiple photos (see Select multiple pictures)
Click on "More options" (three-dots icon)
Select "Edit date & time"
In bulk before you upload, for example using the Picasa 3 desktop application:
Select the picture(s)/movie(s) you want to change the date of
See How to select multiple pictures/movies
Go to "Tools" "Adjust date and time..."
If you want to use the "File creation date" to populate the "EXIF date taken", you can use this (free) tool: http://www.relliksoftware.com/exifdatechanger/download
You cannot change a geotag that is added to the photo before uploading, but you can add a geotag if there is not one:
Go to photos.google.com
Select one or more photos (see Select multiple pictures)
Click on "More options" (three-dots icon)
Select "Edit location"
Add the name of a location that is also found in Google Maps.
I also found that you can add some but not all addresses.