It will depend on whether you are using iCloud Photo or not.
If you are not using iCloud Photos it is easier to back up your Photos, because then you just have to copy the library to your external drive. If iCloud Photos is enabled, the library may not contain all photos and you would need to download the photos and videos from download.
To copy your Photos Library to your external drive, follow the instructions as described here at this link:
Move your Photos library to save space on your Mac - Apple Support
It is essential to prepare the external drive exactly, as described at the link, or Photos may not be able to use the copy of the library:
- The file system format needs to be macOS extended (Journaled) or APFS - please check the file system format - if the box says "formatted for Mac" it may not suffice.
- The drive needs a wired connection, do not get a NAS or any volume, that is accessed remotely over the local network.There should not be any backup software installed on the external drive, you need an empty drive.
- Do not use the same drive for Time Machine backups.
Once the external drive is ready and mounted, create a folder on the new drive, quit Photos, if it is running, and just drag your Photos Library from the Finder into the folder on the new external drive and wait for the copy to finish.
To check, if the copy of the Photos Library can reopened, double click the copy of the Photos Library to open it in Photos and browse it.
Then quit Photos again and double click the original on your internal drive, to switch back to your main Photos Library.
If you should have iCloud Photos enabled, save also the photos themselves, because there may be incomplete items in your library. In that case select your Photos in "All Photos" and use the command "File > Export > Export unmodified Originals" to export the photo to a folder on the external drive. I would not select more than thousand photos at once to export them. Sometimes it can cause problems, if the export is too large.
I am using these Export Settings, when saving my original image files:
The Subfolder format "Moment Name will group the photos taken at the same day at the same location into subfolders, named by the place and the date, so it will be easy to find the photos we are looking for. And "filename: Use filename" will export the image files with the same name as set by the camera. that will make it easy to sort them chronological by the image numbers.
The checkmark by "IPTC as XMP" will create a sidecar file with the metadata. This will save titles and other metadata you added. Keep the XPM files together with your images in the same folder.
