The rules by security people have changed some on remembering passwords over time. We have moved to a time now that most people have a number of passwords they must remember for different sites. You have at least one email password, a password for Amazon, password for your bank, password for other places, If you take classes online a password for there. I recently counted and I have about 25 passwords for the Internet. It used to be they said do not write down passwords but that is no longer realistic. The thing to do is the password not be stored close with name of site and username.
First couple things not to do with passwords. One do not make them a simple word, that is easy for hackers to break. Secondly do not write them on your monitor or on a piece of paper stuck under the keyboard. First place someone looking for your password will look. Third do not use password as your password. About 50% or more of passwords are password. Easy to guess.
Now how to remember them. If you get to choose our password (which most sites do now) make it something you can remember. You could make a word you can remember but change capitalization, change certain letters to numbers or special characters like a to @, e tto 5, I to 1 etc. You could also choose a phase and use the first letter, I could choose I teach computers at GNTC in Lafayette Georgia and make it itcagilg or more secure as 1tc@G1lg
Another thing I encourage is make your passwords for different sites different. You put something about the site in the middle of the password, for instance google for Google or Yahoo for yahoo. Then if password stolen or site is hacked and hacker gets passwords and usernames yours only works for that one site so only one password to change. You can also write them down. However, do not put where it goes to and username clear on same thing and keep away from computer. So you could keep the passwords in your wallet with some abbreviation for the site. Most sites now use your email address as the username so that is easy to remember. Make it a multipart process for someone to be able to determine your password and the username and site. Putting password for work on the monitor is simple for them as they can get username and know password easy. Just like do not put the pin number for your ATM card in your wallet with your ATM card.