You can crochet a bag with all kinds of yarn but if you want your bag to be stable, durable and keep its shape, you should use yarns designed specifically for bags.
This particular bag can be crocheted with polypropylene, polyester or cotton cords, or a mixture of these materials. Raffia is also a material that will have good results. The type of yarn and the size of the crochet hook used will determine the size of the bag.
You should use a good quality ergonomic crochet hook and hold it as you would hold a knife when cutting.