Let's say the model $\alpha$ consists of $(A, a(R_1), a(R_2)...a(R_n))$, where A is a finite set, and all $R_i$ are relation symbols, $a$ denotes their interpretation in the model. I need to prove that a sentence $\phi_a$ exists, which satisfies the following for any model $\beta$:
$$\beta \models \phi_a \iff \beta \cong \alpha $$
Also, let's denote the elements of A as $a_o, a_1... a_n$
The guide says to start by constructing a formula $\psi$, telling which relation each string of elements belongs to (using free variables $v_o... v_n$ and quantifiers). But I am not exactly sure how to do this and how it relates to the question.