This is really easy:
Just like a DM may telegraph the presence of traps and secret doors while describing the environment so that the players can act to have their players find them, in a social interaction, the "traps" are lies and the "secret doors" are the NPC's ideal, bond, flaw, and agenda.
So as DM you just telegraph those lies, ideals, bonds, flaws, and agendas while describing the interaction. From there, the player may have a sense that the NPC is lying or what those ideals, bonds, flaws, or agendas are. To verify those assumptions, the player then says something like, "I'm hearing what she's saying and I get the sense she's not really trying to help the king here... I'm going to try and read that from her body language, speech habits, and change in mannerisms to see if I'm right."
At that point, the player has described what he or she wants to do in a reasonably specific way that allows the DM to adjudicate the action. If there's an uncertain outcome and a meaningful consequence for failure, the DM calls for an ability check, in this case, probably a Wisdom (Insight) check. The uncertain outcome might be because the NPC is trying to hide her true intentions. The meaningful consequence for failure might be that the NPC realizes the PCs may be onto her and thus break off the interaction or become guarded, making all subsequent attempts to figure her out harder.
If the PC is successful, the NPC's agenda is revealed and now the player might have the character use that knowledge in an advantageous way to influence the NPC, granting advantage to any subsequent related Charisma check.
This isn't about reading the DM's mind. It's just adequately describing the environment as a DM, paying attention as a player and describing what you want to do, and then the DM following the standard procedure for play as laid out in the rules. And to bring it around to the original topic, as a player here, I'm NOT asking to make an Insight check. Because if I've paid attention and made a good case for why I think the NPC's agenda is something other than what she has stated, the DM might just tell me I succeed with no roll and no chance of incurring the cost of failure.