How can I compute the cardinality of $\mathcal{O}_K/\mathfrak{p}_i$?

Question

Given a finite field extension $K/\mathbb{Q}$ with associated ring of integers $\mathcal{O}_K$, how can I find the cardinality of the finite field $\mathcal{O}_K/\mathfrak{p}_i$ where $\mathfrak{p}_i$ lies over $(p)$ and $$ (p) = \mathfrak{p}_1^{e_1}\cdots p_n^{e_n} $$ For example, I want to be able to compute the finite field from $$ \frac{\mathbb{Z}[x]}{(x^2 + 1, 2-x)} $$ where $$ (5) = (2-i)(2+i) $$

Answer 1

In the Gaussian integers you could just calculate the norm, $N(2-i)=5$ (Note that $(2+i)(2-i)=5$ not 3!)