There are several methods used for writing braille. These include the Perkins braille writer (often called a brailler); slate & stylus; portable note taking devices; and braille embossers used with specialized computer software.
A Perkins braille writer has several parts and there is a specific process for loading (or putting) paper in it. See a diagram of the braille writer and instructions for using it.
The Perkins braille writer has not changed much in the last 100 years. Think of it as a typewriter. When you push down on the keys, the embossing head makes indentations on the paper. If you're curious, find out more about the history through this link about the evolution of this machine.
Most young children who are potential braille readers have their first exposure to the braille writer during the preschool years. They need to have opportunities to explore it and to "scribble" with it (push down on the keys and make noise and braille). Having a braille writer in the home is ideal, because your child can begin to use it well before formal instruction in reading and writing begins.
A slate and stylus is a portable tool used for writing braille.
Reference -- Here is a complete list of the letters of the alphabet and contractions (short ways of writing words or parts of words). This list is posted with permission from the National Braille Press. A large print copy of this chart can be purchased from NBP.