The analyst breaks down all the film for special teams. Who is in to block, how do they line up, where to attack, how does a team set up for returns, every single detail of the special teams plays.
Then develop a plan to defend or attack what was found. Exploit weaknesses, give special attention to their special plays/players.
This is all in detailed report and the coach on the field then puts the plan in action during practice. I am guessing there is also a video of the other teams ST plays and yours from previous weeks.
A guess.