How to compute denominator in Naive Bayes?
in the Examples section of the Wikipedia article there is a nice example.  The calculation of $p(\mathbf{x})$ can be done via

$$p(\mathbf{x}) = \sum_k p(C_k) \ p(\mathbf{x} \mid C_k)$$

Note that using the conditional independence assumption of the Naive Bayes one can write

$$ p(\mathbf{x} \mid C_k) = \Pi_{i} \, p(x_i \mid C_k) $$