The most iconic piece of ballet equipment is, of course, the tutu and it's what most people will think of when they think of ballet. The tutu is worn to give maximum leg movement whilst dancing and provide a very elegant look as the ballet dancer performs. In a practical sense it tells the dancer roughly where their arms need to be when they are placed in first and second position and they use it as a line of sight for these arm movements. They're also beautiful and because costume is a large part of ballet performances you have find some wonderfully elaborate tutus on famous dancers when they perform.
The next item that features highly on a dancer's list of things is the shoes. For practise these are made of soft leather and are very durable to allow for long term use when training. However, for performances or examinations these shoes are made from delicate and soft satin and when ballet dancers are touring they often need to replace their shoes after just a few performances as they wear out so easily. This is especially an issue when the dancers dance en pointe, which is dancing right up on the toes. To do this the dancer wears shoes that have wooden blocks in the end to balance their toes on. Whilst this is painful the first few times and can often lead to broken toes if they fall, these shoes are what allow the ballerinas to really do the impressive moves that make their shows so popular. You can't, for example, execute a proper pirouette without en pointe shoes.
When training the dancers wear a comfortable leotard and pink or black tights depending on their level and when the dancers are younger they often have a flared skirt with their leotard to train them how to hold their arms. As they get older and more experienced this can change to either a simple belt on the waist or a longer, tulle skirt if they train at a proper ballet school. Of course a nice pink bag to hold all this in as a must have, and a typical ballet dancing bag is a stiffened oval bag with a small handle that fits your shoes, leotard and tights very easily. For children these often have pictures of fairies or ballet dancers on.
Now they have the outfit they need the training equipment. Ballet is all about movement, so of course ballet studios are often huge and have lots of space for big movements and dances. For warm ups or barre exercises, a simple wooden bar along the wall, called a barre, is used. Often one hand is placed on this and simple foot routines are completed. This can also be used for stretching and warm up and cool down routines before and after practise. A mirror is also a key piece of equipment in the room and often an entire wall is devoted to this so that the dancers can see their full body as they dance and can control their movements accordingly.