How to update my iPhone to iOS 15?

You cannot pick and choose an iOS version. What you get is Settings > General > Software update > [All options are available here]

You need to correctly Identify your iPhone model - Apple Support

These are the iOS options based on iPhone Model -->

• iOS 16.3.1 —>
  • Chipset A11 - 8 (2GB RAM) / 8 Plus (3GB RAM) / X (3GB RAM)
  • Chipset A12 - XR (3GB RAM) / XS (4GB RAM)/ XS Max (4GB RAM)
  • Chipset A13 - SE (2020) (3GB RAM) / 11 (4GB RAM)/ 11 Pro (4GB RAM)/11 Pro Max (4GB RAM)
  • Chipset A14 - 12 Mini (4GB RAM) / 12 (4GB RAM) / 12 Pro (6GB RAM) / 12 Pro Max (6GB RAM)
  • Chipset A15 - SE (2022) (4GB RAM) / 13 Mini (4GB RAM) / 13 (4GB RAM) / 13 Pro (6GB RAM) / 13 Pro Max (6GB RAM)
  • Chipset A16 - 14 (6GB RAM)/ 14 Plus (6GB RAM) / 14 Pro (6GB RAM) / 14 Pro Max (6GB RAM)
• iOS 15.7.3 —>
  • Chipset A9 - 6S (2GB RAM) / 6S Plus (2GB RAM) / SE (1st Gen) (2GB RAM)
  • Chipset A10 - 7 (2GB RAM) / 7 Plus (3GB RAM)
• iOS 12.5.7 —>
  • Chipset A7 - iPhone 5S (1GB RAM)
  • Chipset A8 - iPhone 6/6 Plus (1GB RAM)
• iOS 10.3.4 —>
  • Chipset A6 - iPhone 5 (1GB RAM)
• iOS 10.3.3 —>
  • Chipset A6 - iPhone 5C (1GB RAM)
• iOS 9.3.6 —> iPhone 4S (512MB RAM) - Chipset A5
• iOS 7.1.2 —> iPhone 4 (512MB RAM)- Chipset A4

Know how to...

• Update Over-the-Air (OTA) —> Update your iPhone or iPad - Apple Support (IN)
• Update using iTunes/Finder —> Update your iPhone, iPad, or iPod touch - Apple Support (IN)

You don't write which iPhone you have, but below you can see your options. It is not possible to update/downgrade your iPhone to a version before or after those mentioned below.

• Your iPhone 5S/6 can be updated to: iOS 12.5.7
• Your iPhone 6S/7/SE 1.Gen can be updated to iOS 15.7.3
• Your iPhone 8 or newer can be updated to: iOS 16.3.1

You can check your current version here:

Settings → General → About

You can download and install software updates here:

Settings → General → Software Update

Remember to connect to Wi-Fi and a charger. Your iPhone must have more than 50% power to update without a charger connected.

You can find more useful information here:

Update your iPhone or iPad - Apple Support

If your iPhone or iPad won't update – Apple Support (UK)

If you want to update your iPhone via a PC or Mac, see here:

• Mac: Update your iPhone, iPad, or iPod touch with the Finder - Apple Support
• PC (iTunes): Update your iPhone, iPad, or iPod touch with iTunes - Apple Support