The crochet hook obviously is going to be the most important tool you are going to be using to crochet. All crochet hooks are not created alike, so here are some basic features of a crochet hook that you need to know to decide the type of hook that you want to use. The choice of type of crochet hook to use is personal, with no right or wrong answers, so please experiment with the different variations to decide which ones you like best.
A crochet hook has a head, a throat, a shaft, maybe a thumb rest, and a handle. The head will be either round or flat (also called "in-line"). Some crocheters prefer the round head because it is a little pointier and makes entering stitches easier; some prefer the flat head because it can make catching and pulling through the yarn easier. The throat of the hook starts from the indent of the head and tapers to the round, uniform part of the shaft. Whether the hook has a round or flat head, it is the width/circumference of the shaft that determines the size (which is labeled with either a letter and/or number and/or millimeters) of the hook and thus the size of the stitches you make. The shaft measures about 1 to 1 1/2 inches from the head to the thumb rest (if there is one). Many hooks have thumb rests or an indentation at this location of the hook to make the hook easier to hold and to keep the hook from shifting in your hand while you are crocheting.
The remaining part of the hook is called the handle, and a regular crochet hook has one that is about 6 inches in length (compared to a Tunisian/Afghan crochet hook, which is usually much longer).
(Here's the Facebook video)