  We extend to the function field setting the heuristic previously developed,
by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and
ratios of $L$-functions defined over number fields. Specifically, we give a
heuristic for the moments and ratios of a family of $L$-functions associated
with hyperelliptic curves of genus $g$ over a fixed finite field
$\mathbb{F}_{q}$ in the limit as $g\rightarrow\infty$. Like in the number field
case, there is a striking resemblance to the corresponding formulae for the
characteristic polynomials of random matrices. As an application, we calculate
the one-level density for the zeros of these $L$-functions.
