Download a password manager like Keepass, Lastpass or Password Safe:
https://en.wikipedia.org/wiki/List_of_password_managers
I use Keepass, it does exactly what I need.
Secure the password manager itself with a long password. Put your logins into it, and generate a unique random password for each one, then go to the website in question and change the password to the new one.
When you want to login to that website, open your password manager, copy the password to your clipboard and paste it in. Remove the password from the clipboard (Keepass does this automatically after about 10 seconds).
That is ALL you need to do. You could get into using keys, etc, to secure the password manager but if you have a long, unique password for the password manager, it shouldn't be necessary. I'm sure others can provide you with info on how to finesse the process using online password managers, etc, but what I've just described is the basics. Start simple, ramp it up later if you're the paranoid type (which you should be ;)
EDIT: Another thing, if you can use two-factor authentication, do it. I use this on my Google accounts, Paypal and my bank.
https://www.google.com/landing/2step/
https://www.turnon2fa.com/tutorials/how-to-turn-on-2fa-for-p...
Another edit: You can store more in the password manager than just passwords. I keep a scan of my signature in there in case I have to put it into one of those (admittedly insecure) PDF-type forms to "verify" I've signed something. I also make up stupid answers to password hint questions and these also go in the password manager, e.g. "First school" -> "Dr Magnus Pike's School for Aspiring Arsonists". Too easy for people to work out what my real first school is called.