To be able to train in Taekwondo you do not initially need much in the way of equipment. You will need your own dobok, and you will earn your belts as you progress through your grading syllabus and pass each grading.
As you progress you will most likely want to invest in your own sparring gear. There are a number of different things you can buy, but if you want to compete in competitions you will need: a head guard, sparring gloves, sparring feet, gum shield, and if you are male a groin guard. You can also get shin protectors, arm protectors and chest guards.
If you are setting up your own club you will most likely want to invest in Taekwondo equipment that will aid your pupils. This can include a wooden horse (to practise breaking), plastic breaking boards and wood breaking boards. It will also be useful to have focus shields and focus paddles for your students to use whilst practising sparring techniques.
You can also get Taekwondo equipment such as ankle supports, knee supports, elbow supports, training bras, training tops (to wear under your dobok), training shoes and Taekwondo books and Taekwondo DVDs to help your studies of this martial art.
This is by no means an exhaustive list but hopefully it should provide you with an indication of the different Taekwondo equipment that is essential and those that you will find useful.