It's actually easier to memorize a randomly generated password than you'd expect. Initially you'll want to have it written down on a piece of paper you carry with you, but it takes less time than you might think before you no longer need that written record. My master password is a 20-character string of upper- and lowercase letters, numbers, and symbols, but I remember it very clearly. (It helps not to need to remember dozens of other passwords, too.)

Beyond that, password managers are just really convenient. I never have to do a "forgot password" thing on any website anymore, and the autofill functionality is really, really nice. At this point I honestly don't know how I lived without one for so long.