Showing that stalk $O_{Spec \ A, p}$ is $A_p$

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Suppose I have $A$, a commutative ring with unity. I would like to show that stalk $O_{Spec \ A, p}$ is $A_p$ for $p \in Spec \ A$. Could someone please explain me how this works? (I am having trouble showing that the map from $O_{Spec \ A, p}$ to $A_p$ is well defined.) Thanks!