Arduino calculator: I'm struggling to write a sketch which parses inputted characters
Characters in a char[] variable may be encoded in ASCII or Unicode. You will want to convert them to numbers in this case. Consider subtracting the ascii value of one less than 0 from each char to get the number. Edit: @Matt informed me that 0 is the lowest ASCII number. As he suggested, you can subtract the character '0' from the digit to get the value. You want to specially handle any addition, division, or other operator symbols.

Then you can treat each number like a digit in a number. If you can break up the array of numbers by the operators, you can successively attach the operands to the operators. Keep in mind that each number to the left is a power of ten (assuming this is how it's implemented. This is called Endianess.)

If you post code I may be able to help further.