Identifying and describing the language accepted by a Turing machine
A Turing machine implements an algorithm.
The algorithm can be implicit by an explicit definition of the language such as:
$M$ is a TM such that $L(M)=\left \{ x\in \Sigma^* \ | \ |x|\in \mathbb{N}_{even}\right \}$. Which is usually the case.
In other cases, you might have to understand a turing machine based on a state diagram, this will be a simple reverse engineering problem where based on some inputs you understand the algorithm (and then you can prove your assumption).
Generally, there is no fixed approach towards understanding the language a machine accepts.