steps to replace dead Apple Watch with a new one?

Are you asking how to get a new device? Or are you asking how to set up a new device you already have?

If the former, you can start here if you want to see if it can be fixed:

Apple Watch Service and Repair - Apple Support

Or, you can buy a new one.

If you're asking how to set up the new watch, start here:

Set up your Apple Watch - Apple Support

You will be given the option during the set up process to use the backup from your previous watch.

Hmm, buy a new one?

Or are you asking how to get a service replacement from Apple?

You would only get a replacement from Apple if you had Apple Care+ on it, and you pay the service fee / deductible.

click here ➜ Apple Watch Service and Repair - Apple Support

There is no way to get a free replacement if that is what you are asking.

Try the following:

1. On a computer, go to Find My iPhone on iCloud.com and sign in with your Apple ID.
2. Select All Devices, then click your Apple Watch.
3. Click Erase Apple Watch. Select Next until the device is erased.
4. Click the X button next to your Apple Watch.

What to do before you buy, sell, give away, or trade in - Apple Support