The document provides instruction on performing the order of operations when simplifying expressions. It recommends following the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to determine which operation to perform first from left to right. Parentheses are used both for grouping elements and for implied multiplication. When there are subtraction and addition terms, subtraction is performed first if it appears furthest to the left. Similarly, with multiplication and division terms, the operation furthest to the left is performed first.