Balance chemical equations by adjusting coefficients so that the same number of each type of atom appears on both sides, without ever changing a subscript.
A chemical equation is a shorthand sentence describing a reaction: reactants (the starting substances) on the left, an arrow meaning "produces" or "yields," and products (the new substances formed) on the right. The law of conservation of mass says atoms are never created or destroyed in a chemical reaction, only rearranged -- so a correctly written equation must show exactly the same number of each type of atom on both sides.
Balancing an equation means adding coefficients (whole numbers placed in front of a formula) until the atom counts match on both sides. The one absolute rule: NEVER change a subscript to balance an equation -- changing a subscript changes what substance the formula represents entirely (H2O is water; H2O2 is an entirely different substance, hydrogen peroxide). Only coefficients, which show HOW MANY of that whole formula you have, are allowed to change.
A reliable method: write the correct, unchanged formulas for every reactant and product first, then balance one element at a time, usually saving the element that appears in the most different formulas for last, and double-checking every element's count on both sides at the very end.
Mastery looks like: They correctly balance chemical equations using only coefficients, and verify their answer by recounting every element on both sides.
Common stumbles: Changing a subscript to try to balance an equation; forgetting to recheck ALL elements (not just the one just adjusted) after changing a coefficient.