it's an honest question
they take a map, work on ideas with assistent coach(es) then test them in reality with the team during scrims, see how well they do and work on new strats constantly
work on individuals in the team, work on their player's mental and physical skills, work on their form
they mostly are the ones that do anti and generally understand the game to the highest level, thats why you see things like potter timeouts which make the team look completely different and much, much better
very hard to see the positive impact of coaches other than people like engh, potter, ex6tenz, mini, solo etc but a bad or mediocre coach is always painfully obvious to see and very, very had to fix
Before the match: Devise team comps and strats for different maps and test them out against other teams (If they are tier 1 teams they'll usually scrim against decent T2 teams in the region). If the coach finds that the team struggles on a certain map they will select that as their permaban. They may also review VODs of the team they face up against, see how they play out certain maps, and devise strats to counter the enemy team (anti-stratting). They also usually serve as a counselor to maintain the players' physical and mental health to keep them in the best playing form.
During the match: Watches the gameplay and analyzes how both their team and the enemy team play out certain rounds. If they notice anything the players should capitalize on they'll call timeouts. Coaches also call timeouts to give the players a mental reset if the webcams show noticeable distress.
After the match: Review the VOD and spot out any errors in either IGL calling or timeout calling. This feedback is then applied to the next match.
On your question about fraud coaches, those kind of coaches will not call timeouts (Termi), put players on non-comfort roles (LEGIJA), allow permaban maps to go through (Chet), and overall puts the team at a strategic disadvantage.