You will need at least four dice. Four per person is best. Fate (sometimes called Fudge) dice are what the game uses, but regular six-sided dice work too. Or you can use an app (I like "Nice Dice" by Lost Minds).
You can use playbooks on a phone/tablet screen, but printing them out is best.
Tokens of some kind (heck, you can use cheerios) are required to represent fate points.
Finally, it's good to have scraps of paper or index cards for writing down aspects.
For more, you can watch my favorite primer on Fate games, that being the one Tabletop did this summer: https://www.youtube.com/watch?v=NOFXtAHg7vU