How do I set up my new iPhone 13 and transfer data from my old iPhone 8?

What do you have available for you to do that? A PC with iTunes loaded or a Mac with Finder is my preferred method. It would also require a Lightning cable that connects to the computer. The process would be to create a backup to the computer, then restore to the new device from that backup. The process is slightly different on a PC because there is no built-in access to Apple devices like there is in Mac's Finder.

To back up to a computer:

How to back up your iPhone, iPad, and iPod touch with your Mac - Apple Support

How to back up your iPhone, iPad, or iPod touch with iTunes on your PC - Apple Support

And to restore (or set up) from the backup.

https://support.apple.com/en-us/HT204184

Another method is wirelessly through Bluetooth, although I haven't tried it myself.

Use Quick Start to transfer data to a new iPhone, iPad, or iPod touch - Apple Support

Then there's iCloud, but I wouldn't be able to do that myself because I don't have enough iCloud storage.