The bare minimum you need to crochet is a hook and yarn, but adding some other supplies to your kit will make your work much easier.
taken from http://www.yarnforward.com/crochetconv.html
taken from http://www.yarnstandards.com/weight.html
Scissors
You'll need scissors to cut the yarn when you've finished your project or when you're switching colors.
Ruler or measuring tape
You'll need a ruler to check gauge before starting a project. Sometimes you'll also be asked to continue a certain part of the pattern for a certain number of centimeters or inches, so you'll need a ruler to check your distance.
Patterns
Patterns are essential for any beginning crocheter. They describe how many of each type of stitch is needed to complete a project. They also give information on gauge. Once you learn the basics of crocheting, you can design your own patterns, too.
Yarn needle
Yarn needles are thick, blunt-ended needles (often plastic) with large eyes that are used for weaving in the yarn ends when you've finished your project.
Stitch markers
Needle
You'll need a needle if you're sewing any embellishments onto your finished crochet work.