How do we get ${}_0$ and ${}_1?$

Let $(x_i,y_i)$:$1,$dots,$n$ denote a random sample of size $n$ from the population.

$y_i={}_0+{}_1{x}_i+u_i$

The method of Ordinary Least Squares $($OLS$)$ chooses the estimates to minimise the sum of squared residuals.

That is$,$

min${\displaystyle \underset{i=1}{\overset{n}{}}}(y_i-$hat$({)}_0-$hat$({)}_1{x}_i{)}^2$