Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrr} & x^2 & \\ \color{blue}{ + } & & 1 \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrr} & x^2 & \\ \color{blue}{ + } & & 1 \\ \hline & x^2 & 1 \end{array} $$