To export your Google photos you will have to visit the website for Google Takeout which can be found at this link.
The Google Takeout Page will look like the image below:
Click Deselect all, then scroll down the list to find Google Photos and tick the box next to it.
Scroll all the way down to the bottom of the page and click the Next Step button. Then you will have to select the transfer method and file type from the dropdown box:
Click Create Export and the Export Progress Box will be displayed as in the screenshot below:
Depending on the amount of files to be transferred this process can take some time. You will receive an e-mail when the process is finished.
Click the download link in the e-mail and your files will download to your computer.
After the photos are downloaded to your computer you can upload them to a personal google drive or other cloud storage solution. You can also back them up to another hard drive or external backup device, instructions on how to do that can be found at this link