See demo.cpp, it is really straightforward:

• You construct a TableState object from a fen string using get_table_state.
• If it was valid (check value returned), you can call some functions like:
  • is_king_in_check
  • is_checkmate
  • get_draw_reason
    • Returns enum of draw reason.
  • is_move_invalid
    • Returns enum of invalid reason.
  • apply_move(TableState*,const char*)
    • Returns a new table state. Check beforehand if move is valid, unexpected behavior if not!