Restriction of Cartier divisors

Question

Let $X$ be a smooth variety, $D=\{(U_{i},f_{i})\}$ a Cartier divisor on $X$ and $V$ a closed subvariety of $X$. Define $D|_{V}$ as the restriction of $D$ to $V$.

I have two questions:

1. When is $D|_{V}$ a Cartier divisor?
2. When $D|_{V}$ is a Cartier divisor, how does one write it down in the form like $D$?