Assume our modal language $L$ has only diamonds, and the set of proposition letters $Prop$ is finite. The deduction rules are the same as normal modal logic. Now consider $M$ is a finite model of this language $L$. We first define an equivalence relation $\approx$ on $M$ : $u\approx v$ $\Leftrightarrow$ $M,u\models\varphi$ iff $M,v\models\varphi$ for every $\varphi\in L$. Since M is finite, we then have finite $\approx$-equivalence classes $M_1$, $M_2$,..., $M_n$.
Now the question is: how to construct formulas $\varphi_1$, $\varphi_2$,..., $\varphi_n$ such that for every $i=1,2,...,n$, for $u\in M_i$, we have :
$M,u\models\psi$ iff $(\varphi_i\rightarrow\psi)$ is a $L$-theory, for every $\psi\in L$.