While each inkmaker has his own special formula, most writing ink are generally made the same way.  The inkmaker dissolves special dyes in purified water to get the desired color of ink.  The he adds certain acids and salt to make the ink permanent

The inks used in ballpoint pens are different from ordinary writing ink.  Ballpoint inks are thick liquids as heavy as syrup.  A small ball in the tip of the pen rolls the ink onto the paper.  Ballpoint inks contain more dye than do ordinary inks to ensure that the ink can be rolled out in a very thin line and still make a good mark.

The first inks were made from water colored with berries and other plant juice.  A long-lasting black ink, much like the dense black ink used by artists today, was made by mixing smoke soot or charcoal with animal glue or certain gums such as gum arabic.

an image of a Chinese inkstick via Wikipedia

The mixture was poured into a mould and allowed to dry to form a solid piece.  When it was to be used, water was added.  People wrote with a brush dipped in the ink.

They dried the ink with a sprinkle of sand.