Giving a regular grammar for the language
That's fairly easy. Just take a non-terminal X and add the rule $X\to aY$ where $a$ is the label on the arrow from $X$ to $Y$ if $X$ is not final; if it's final add a rule like: $X\to \epsilon$ as well. Do that for every non-terminal and you get a right-regular grammar.

Here is a right-regular grammar for the given automaton:

$A \to 1 A$

$A \to 0 B$

$B \to 1 A$

$B \to 0 C$

$C \to 0 C$

$C \to 1 C$

$C \to \epsilon$