Let $G$ be a finite group and let $\lambda$ be de left regular representation of $G$ of $\mathbb{C}$, i.e. $$\lambda_g : h \mapsto gh \text{ for all } h \in G.$$ Specifically, for any function on the group $f: G \to \mathbb{C}$ we have $$(\lambda_g f)(x) = f(g^{-1}x).$$
A representation is said to be reducible if we can write is as $$D(g) = P^{-1}\lambda_gP,$$ where $D(g)$ is a block diagonal matrix containing irreducible representations, i.e. $$D(g) = \begin{bmatrix}\rho^1(g) & 0 & \cdots & 0 \\ 0 & \rho^2(g) & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & \rho^k(g) \end{bmatrix}.$$
How do I find these irreps and $P$ for a given group, let's say the $D_n$ group? Moreover, are these irreps/$P$ unique?