The main thing to keep in mind when playing mafia is that the mafia must lie in order to remain undetected in the town. This means that town's strategy revolves around questioning mafia and trying to find holes in their reasoning.
As a mechanics example, if a mafia member is asked what their action was at night, they would be revealing themselves if they truthfully answered, "I killed [person]." So, the mafia has to come up with a lie for their night action that would not be easily seen through by the town. The town may be able to use investigative roles to leverage information against the mafia in this situation.
As a social example, a mafia member probably doesn't want to vote for their fellow mafia in the daily vote. However, the town may be able to spot that these two members are refusing to vote for each other, which might indicate that they are mafia. This is why questioning people's opinions is helpful for town: it might reveal two mafia members that are connected to each other, or that one mafia member is trying to deflect suspicion off another. Conversely, as mafia, you need to try to manipulate the town into believing that you or your fellow mafia is innocent, and try to place suspicion on a member of the town.