How do I install Apple Intelligence on my new iMac M3?

To turn-on Apple Intelligence on a Mac, you can do the following:

1. Update to macOS Sequoia 15.1 
2. Go to the System Settings menu 
3. Click Apple Intelligence & Siri 
4. Click Join the Apple Intelligence Waitlist 
5. Wait for a notification that Apple Intelligence is ready for your device 

Upgrade to macOS Sequoia 15.1, or presumably anything that may supersede it in the future.

General requirements: How to get Apple Intelligence - Apple Support

You just need to install Sequoia if it's not installed already. Then open System Settings > Apple Intelligence & Siri.