The ingredients to make India ink are char (wood and bone were traditionally used), water (or water with drops of vinegar for stability) and a binder such as shellac, gelatin, agar-agar, a gum or resin. You can also use lamp black from an oil or kerosene lamp. Note that these burned items contain carcinogens so take precautions like wearing gloves and not breathing in their dust.
Full instructions for making India ink are here.
The ink produced by these instructions can be kept in liquid form or dried into cakes for use with a brush (as for Chinese and Japanese calligraphy).
Here is Lemoine de Gascogne in Texas making bone black from pieces of deer bone: