How can I upgrade my iPhone 6s iOS13 to iOS 15?

Go to Settings/General/Software Update and follow the instructions. To update over the air from the phone all of these requirements must be met:

• You need at least 10 GB of free storage for iOS 16 or 6 GB for iOS 15 or lower; more is better
• You must be connected to a Wi-Fi network (and not a personal hotspot)
• The phone must be charged to at least 50%, and preferably plugged in so it stays above 50% during the update
• The phone must not be in Low Power Mode
• The phone must not be connected through VPN, and it may be necessary to delete any VPN apps and VPN profiles
• The phone cannot be in Airplane mode and must have a cellular data connection
• You cannot still have a beta version installed on the phone<—You may have an iOS 13 beta
• You cannot have a previous version that was downloaded, but not installed - go to Settings/General/iPhone Storage to look; if you find an iOS installer, delete it

If you can't meet all of them you can still update using your computer.

Hello,

There are different ways to ensure the highest iOS that your device will support is installed on your device.

An iPhone 6S through 7, or SE(gen. 1), will currently update to iOS 15.7.5

This support article has instructions about updating an iPhone or iPad wirelessly --> Update your iPhone or iPad - Apple Support

You can also use Mac and PC computers to update system software:

Update iOS on iPhone - Apple Support

When updating, your device will update to the highest version currently available that it will support, or it will just say it is up to date (and can't go any higher) and won't install anything. Apple indicates ( Unable to update my iPhone 6 Plus from 12… - Apple Community ) I need to point out the obvious and state that if you want to run a higher system version than your current device will run, that you need to buy a newer device.