Start with the addition. How did you learn it in school in the very early educational levels? How do you do it on paper without shortcuts or memorization?
From right to left, you add the two digits (you will unfortunately HAVE to convert at least the digits to numbers for this) and if the result is two digits, use the first digits (the right-most one) as the current new digit's value, and the second digit (the left one) to be added in the next pair of digits.