I want to update my iPhone software to iOS 15

Assuming you have a compatible device, see: Update your iPhone, iPad, or iPod touch - Apple Support

And: If your iPhone, iPad, or iPod touch won't update - Apple Support

If the above Apple articles do not help, please post back with relevant information. 

The iPhone 5S/6/6plus cannot update further then iOS 12.5.5

The iPhone 5C cannot update further then iOS 10.3.4

The iPhone 4S cannot update further then iOS 9.3.6

The iPhone 4 cannot update further then iOS 7.1.2

If you have an iPhone 6S or later and updating wirelessly is not working, please update via a pc or Mac instead

Update your iPhone using a Mac with macOS Catalina or higher

On a Mac with macOS Catalina or higher, you will use the finder in order to upgrade your iPhone. Make sure to Back up your device before starting the upgrade process.

On a Mac with macOS Catalina or later, you will follow the following steps:

1. Open a finder window
2. Connect your device to your Mac via a lighting to usb A or a lightning to usb c cable
3. Select your device in the left sidebar of the finder window
4. click general, then click check for update
5. Click download and update.
6. If asked, enter your iPhone passcode

Update your iPhone via a Mac running macOS Mojave or earlier, or on a Windows PC

On macOS Mojave or earlier, or on a windows machine, we won't use the Finder to upgrade your iOS

Instead, we will use iTunes. Make sure to Back up your device before doing any update or upgrade to your phone.

1. Open iTunes
2. connect your device to the computer with an lightning to usb a or a lightning to usb c cable
3. Click device button in the iTunes toolbar
4. In the summary tab, click check for update
5. Click download and update, follow The on screen instructions
6. If asked, enter your iPhone passcode.