Keep your registration with you when you fly
If law enforcement ever asks you for proof you're allowed to fly your drone, you'll need to produce a registration form. However, you don't need to print out a hard copy and carry it wherever you go, since an electronic version pulled up on your phone via the FAA website works just as well.
And re-up every three years
You're fine to fly for a few years once you register, but you need to renew every 36 months, which'll cost you a cool $5 each time.