  We study isogeny classes of Drinfeld $A$-modules over finite fields $k$ with
commutative endomorphism algebra $D$, in order to describe the isomorphism
classes in a fixed isogeny class. We study when the minimal order $A[\pi]$ of
$D$ occurs as an endomorphism ring by proving when it is locally maximal at
$\pi$, and show that this happens if and only if the isogeny class is ordinary
or $k$ is the prime field. We then describe how the monoid of fractional ideals
of the endomorphism ring $\mathcal{E}$ of a Drinfeld module $\phi$ up to
$D$-linear equivalence acts on the isomorphism classes in the isogeny class of
$\phi$, in the spirit of Hayes. We show that the action is free when restricted
to kernel ideals, of which we give three equivalent definitions, and determine
when the action is transitive. In particular, the action is free and transitive
on the isomorphism classes in an isogeny class which is either ordinary or
defined over the prime field, yielding a complete and explicit description in
these cases.
