process each term / token in the expression (operand or operator) one by one. if a token is an operand, push it into the stack. if a token is an operator, pop the stack top item as the 2nd operand and pop the next item as the 1st operand. evaluate the expression and push the result back into the stack. this result will be either the operand for the next operation or, if that was the last operation, the result of the entire postfix notation.