Find closest multiple of $13$ to $25$. We see that $1 \times 13 = 13$ is the nearest. Now subtract $13$ from $25$ to get reminder $12$. Add $1$ to quotient.
Find closest multiple of $13$ to $122$. We see that $9 \times 13 = 117$ is the nearest. Now subtract $117$ from $122$ to get reminder $5$. Add $9$ to quotient.
Since $5$ is less than $13$, stop the division. The reminder is $5$. The topmost line $019$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $19$.