To make a realistic costume beard, apply crepe hair from a costume shop to the face with adhesive. Less realistic beards, especially for use in children's costumes or programs, can be made with cotton balls or yarn.
Crepe hair is actually wool that has been dyed and worked to look like hair. The product, which is often around 12-inches long, can be purchased from some craft shops, ordered online or bought in costume shops. Costumers trim the wool to the desired beard length before applying it to the face with costuming glue. Before applying any item to the face, it's important to shave the area cleanly, as later removal of the adhesive can pull at hairs.
For a quick beard for a child's costume, cut a triangle from a piece of cardstock or construction paper. The triangle should be the size of the desired beard. Cover the triangle with cotton balls. Punch holes in the upper two corners of the triangle and tie yarn or ribbon through the holes. Use the ribbon to tie the beard onto the child's face. For a more complete look, add a mustache-shaped strip on top of the beard, attaching it at the ends to the beard while leaving room for the child's mouth to show through.