How do I look at photos stored on the cloud?

If you have iCloud Photos turned on, the photos on the device are the same as on iCloud, with the possible exception that some of them may be space-saving optimized versions if you have that option turned on. You view them in the Photos app on an iOS device or Mac. You can also login to icloud.com and go to the Photos app there. The following Apple article has information about iCloud Photos: Set up and use iCloud Photos - Apple Support

If you didn't have iCloud Photos turned on but do have an iCloud backup, you can restore the entire phone (not just the photos) from iCloud but you cannot otherwise view the contents of the backup. The following Apple article has information about backup: Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

léonie wrote:

One more thing - if you are not using iCloud Photos on your iPhone and want to see them at www.icloud.com in the Photos Library directly in iCloud in Safari, you have to set Safari to request the Desktop version of the websites, as the mobile version of www.icloud.com is different.

Settings > Safari > Request Desktop version

That used to be the case but hasn't been for iOS versions released the last several years. Also see the following: Which iCloud.com features are available in the browser on your device - Apple Support

P.S. - I'm writing this on my calendar as a historical day that I actually may have known something even remotely related to Photos that you didn't. I don't expect that to ever happen again!

One more thing - if you are not using iCloud Photos on your iPhone and want to see them at www.icloud.com in the Photos Library directly in iCloud in Safari, you have to set Safari to request the Desktop version of the websites, as the mobile version of www.icloud.com is different.

Settings > Safari > Request Desktop version