I need to show that $A$ is countable iff $\mathcal{P}\_{fin}(A)$ is countable.

where $\mathcal{P}\_{fin}(A) = \left \{ x\subseteq A\mid x\;is\;finite \right \} $

I know that if $A$ is countable, I can build an infinite amount of such $x$'s, but its obviously not enough. I am missing the main direction of the proof.

I would appreciate help on this proof