The crochet hook is by far the most important tool you can use in crochet. It is basically a round handle pointed on one end, with a lateral groove behind it. The handle is not always circular, often it is carved and shaped into a comfortable handle. The size of the hook varies greatly depending on the project, and every crocheter needs quite a few crochet hooks of differing sizes. Sizes can be marked by both numbers and letters. Conveniently, most yarns and patterns have a suggested hook size to avoid guesswork. Crochet hooks can be made from plastic, aluminum, bamboo, and some even have special grips to make them more comfortable to hold. Aluminum hooks are probably the most common, and are perfect for beginners.
More information on crochet hook sizes can be found here.
Other materials you might need in your crochet journey are stitch markers, scissors, tapestry needles, and a ruler/tape measurer.
Craft Store/Online Shoping List
Above:A set of crochet hooks in variuos sizes