For getting started with Chinese calligraphy, you will need:
An Ink brush - You can buy Chinese brushes in an art store. Traditionally, Chinese calligraphers used brushes with handles of bamboo, wood, ivory, bone, glass, gold and silver. The brush was made from hair - rabbit, tiger, deer, pig, etc. - or bird feathers - chicken, duck, etc. You can also use a calligraphy pen, but calligraphy with brush is considered more virtuoso.
Paper - You can buy thin rice paper in an art store. It might be best though to practice first on a cheaper quality paper. Traditionally, the Chinese used paper made from rice, bamboo, mulberry and hemp. The best quality came from the Anhui province in China.
Ink - You can buy Chinese black ink in an art store. Traditionally the Chinese used inksticks made from lampblack and binders - the inksticks were rubbed with water on ceramic or stone inkstones until black ink of the required consistency was obtained.
Paperweight - for holding the paper down. Traditionally, the Chinese used many different types and beautifully carved paperweights.
Seals - These are used to sign the work once it is done. Red ink is usually used for a signing seal.
Deskpad - These are used by students and have grids that, when placed under the paper, can be used as reference for getting the size of the characters right.