Here's a recursive descent trick worth mentioning: instead of decomposing expressions into levels called things like "term" and "factor" by the precedence of the operators involved, you can do it all using a while loop:

    function parseExpressionAtPrecedence(currentPrecedence) {
      expr = parseExpressionAtom()
      while op = parseOperator() && op.precedence < currentPrecedence {
        if op.rightAssociative {
          b = parseExpressionAtPrecedence(op.precedence)
        } else {
          b = parseExpressionAtPrecedence(op.precedence + 1)
        }
        expr = OperatorExpression(op, expr, b)
      }
      return expr
    }

The parseExpressionAtom function handles literals, expressions in parentheses, and so on. The idea is to keep pushing more operators on to the end of an expression until a higher-precedence operator appears and you can't any more. This technique (called precedence climbing) makes parsing these sorts of arithmetic expressions a lot less painful.