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To publish an app in either the Play or App store, you must be enrolled in the respective developer programs. The process for enrolling in these is well described in the documentation (Play Console and App Store) and I will not repeat them here.
However, before going through those processes, there are a few things to note:
Apple Developer Program
It costs $99 USD/year to maintain an active Apple Developer account.
A human reviews your application and it will take several days to a week to gain admittance to the program. Some developers report it taking over a week, especially if they are based outside the US. So, you should apply to this program first, to get the process going.
To apply to the Apple Developer program, you need an Apple ID with 2-factor authentication enabled and access to an Apple device (Mac, iPhone or iPad). It is not possible to apply from a non-Apple device.
To start the application process, you must install the Apple Developer app on your device.
After installing the Apple Developer app, open your Account page. Tap the Enroll Now button and go through the application process there. When you are done, the Apple Developer account page will look like this, until your application has been approved.
A final piece of advice: when I applied, I entered my Norwegian home address, but paid with my American credit card (since it was not accepting my Norwegian card). This slowed down my application process because they needed extra verification of my identity. So, if at all possible, try to make everything related to your identity align in your application.
Play Console Account
It costs $25 (one-time fee) to create a Play Console account. Creating an account gives you access to the Play Console, where you can manage tests, and configure and deploy your releases (among other things).
If you do not have a second account for non-personal use, create one now. Using your personal account to publish to the Play store carries some risk. Accounts can be suspended because of violations in the Play store (real or imagined by an algorithm). If you use your personal account and it gets suspended, you would lose access to your personal emails and files in Google Drive etc.
A human will review your application. So, after you have paid the $25 and submitted it, your account is not immediately created. It can take anywhere from a couple of hours to a week.
To apply, sign into Chrome from the google account (gmail or workspace) you wish to associate with your published apps. To apply, click on the "sign in" button on this page. Since you do not yet have an account, you will be redirected to create one on a signup page.
On the signup page, click the Get started option under the Yourself section and follow the instructions to complete the application and pay the $25. (Remember, if you are publishing an app for an organization, this is not the series for you)
After your Play Console account application has been approved, you will recieve an email. From that point, you can log into the Play Console. Read Part 2 to learn about getting your app ready for publication in the Google Play store and uploading it to the Play Console.