What does "how to identify impulse response of a system?" mean?
Given a system, one often wants to be able to predict the output $y$, given an input $x$. This amounts to identifying a mathematical relation between all inputs and outputs, optimaly as $y = S(x)$. This can be a difficult task in general.

When the system is linear, and time-invariant (its properties do not change over time), then it is proven that it  suffices to know the system's response to a discrete unit pulse $\delta$, to be able to compute the output for any other input $x$, in the form of a convolution equation. 

So suppose that your system outputs $h[n]$ when you input $\delta[n]$, then for any $x[n]$, the output will be:
$$y[n] = \sum_k x[k]h[n-k]\,.$$

To identify the impulse response of the system, you ought to provide the numbers, or a generic formula, that give the value for each $h[n]$.

You can try some exercices in Exercises in Signals, Systems, and Transforms, for  instance 1.2.4 and 1.2.7. You can also check the applet in the joy of convolution.

Since, in practice, it is impossible to generate a discrete pulse, there are other practical identification techniques for real-life systems, using random sequences or sine waves.