How to make the impulse response sparse? How does one know that the channel is sparse?
How you parameterize your sparsity will depend on your application.  The authors of that paper, in a paragraph on page 231 say:



which is why they clump the coefficients together in $P$ blocks of start time $t_{B_k}$ of duration $n_{B_k}$.

For one impulse response this is shown in their figure 1(b).



The overall sparsity will depend on the reflections and delays that they have when this impulse response is used by the direct signal and all its indirect reflections.


  How are the impulse response/coefficients made sparse?


You need to decide which coefficients in the overall impulse response are zero. To do that, you need to decide why they are zero (what is the cause?). Perhaps there is a long dead-time between the onset and the first secondary response.


  How does one do parameterization of impulse response to decide for sparse/non-sparse?


Once you've decided on the form, you decide on the structure of the non-sparse parts of the response and how they are separated from each other. 

Suppose your non-sparse parts are all defined by $\alpha_k h[n]$, where $\alpha_k$ is the gain of the $k^\mbox{th}$ non-sparse segment and $h[n]$ is the FIR response of all segments (modulo a gain term). $h[n]$ is of duration $H$.  Then the sparsity will come about by how you space out the $\alpha_k h[n]$:
$$
g[n] = \sum_{k=1}^K \alpha_k h[n-t_{B_k}]
$$
where $t_{B_k} \gg H$ for sparsity to be true (so there is lots of space between the $\alpha_k h[n]$.


  In general, how is parameterization applied to make the impulse response to zero and in general how does one know which coefficients are sparse?


This comes down to how do you choose $t_{B_k}$ and $H$. That will depend on what system you're trying to model.