A piece of paper is a fine method.
Here's what the pros do... it's inferior to paper, in a lot of ways.
Use the
Keepass password manager
This manager uses a secure database file; you enter one password to be able to read that database file. So, instead of having 50 passwords, you have one password to remember, the password to that database file.
Problem: if you lose that database file, you lose all your passwords.
Solution: put the file on a cloud drive.*
Then, you can install the iPhone/Android Keepass port, and tell the app to use the database file from the cloud**. At that point, you have your passwords available on desktop and on your phone, and you can update the database from either location. (Just remember to hit SAVE.)
*You should probably back up the database file locally anyway, in case you don't trust your cloud provider or, more likely, you manage to mungle the file in some other way.
One good way to back up the file is to just print all your passwords. Put the printout wherever you used to keep the paper with all your passwords on it.
**I'm not sure all apps work with all cloud drive providers. Check with your app to see what it supports.