The steps to set up an Android device outlined here are for a Google Pixel phone running Android 12. However, the screens may look rejigged on other phones and older Android versions, but the options themselves won’t be any different. If needed, you can go through the OEM section at the bottom for additional details on non-Google devices. With that out of the way, we can now look at the setup process:

Booting up your phone for the first time will show you a welcome screen with options to pick your preferred language and region and some vision settings. These assistive options include basic things like font and display size, along with some more advanced tools like TalkBack and Select to Speak to help people with vision impairment.
The phone will ask you to set up the networks on the following screens. You can insert a physical SIM card at this stage or download an eSIM (the process may vary depending on your country and carrier). Also, connect to a Wi-Fi network here to restore any backups in the next step.

After having a working internet connection, the phone will take you to the data restoration page. If you have your old phone handy, you can transfer your data wirelessly or using a data cable, but pulling a recent backup from Google Drive is the easiest option. Tap on Can’t use old phone? and sign in to your Gmail account. You should then see the last backup from your old phone. Tap on it, confirm your old phone’s lock screen PIN/password/pattern and select what all you want to restore on your phone. When done, hit Restore. 

While your data restore in the background, the phone will move on with the setup process. Google will next seek your permission for its various services, including backup, location history, and diagnostic data aggregation. All these are optional even though they’re enabled by default, so you can either allow only a few or turn them all off before accepting.
In the final step, you’re suggested to add a security lock to your phone using a PIN or a password that usually accompanies your registered fingerprints as backup unlocking methods. Fingerprint + PIN is the most common combination, but it’s okay if you feel strongly for the good-old pattern lock.

And that’s it! Your phone should be ready to use while Play Store restores and updates your apps in the background.

Google may still want you to check out some of its additional features or finish up anything left in the initial setup. You’ll get a notification to get these last few things sorted. In my case, it was my fingerprint that I didn’t set up earlier, along with the option to enable Google Assistant and other basic things like Pixel’s Now Playing, always-on display, and add another Gmail account.