I am still a fairly new DM. I am wondering what is the best ways you have found to describe the events of certain rolls and skill checks without giving too much away. 

For example, say a player is making an Insight check to see if a certain NPC is lying to them. They roll a 3, so the player knows that their character going to have much insight on the situation. So if I were to describe the outcome as something like "As far as you can tell, this person is telling the truth", then the player would probably still be suspicious of the NPC, even if their character is not, based off of what they know about their roll; because of this I would like to find a better way to describe these sorts of situations

My players are generally good about not meta-gaming in this way, but I would like to make the game more interesting by still leaving things like this as a mystery even for the players if possible. 

So, with this example in mind, I wanted to hear what clever description phrases other more experienced DMs had come up with for situations like these and others. 

The biggest thing you're going to learn is that any ambiguity in a description will lead to the players believing that there is more to the scene than is being revealed.

In your situation the Player rolled a 3 for Insight giving you two ways to resolve the scene, ambiguous or direct.

Ambiguous: "As far as you know, the NPC is telling you the truth." 
This will, probably, lead to the rest of the party asking to roll Insight or the Player asking 20 questions. The answer leads the player to believe that there's more to the situation so they'll do everything they can to get the information they think is there.

Direct: "The NPC shows no sign of deception."
With this there's no way to misinterpret or "read between the lines". It is a very flat answer and, for some DMs, that doesn't feel right because they want the flowery descriptions.

Colorful but Direct: "The NPC looks to you waiting for your response. They're agitated but, you sense they're not trying to deceive you."
Here we have the colorful words and imagery but you're still giving them a direct answer that leaves the player understanding that 'No, there is no deception'. If the player refuses to believe that, it's on them, but you were direct in your response to the roll of the die.

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There are times where being ambiguous will be helpful, but it should be used properly. An NPC who just looks guilty, ambiguous answers will help re-enforce the personality trait. A mission where they have to be political or solve a mystery, ambiguity will help with placing red herrings and false leads. In the end it's part of the narrative, when in doubt, just give a direct answer, it will save you and your players a lot of hassle.

Couple other variations on a low Wisdom/Insight roll for the purposes of hiding deception:

"Her eyes seem confident and focused when she speaks, and you don't notice any hesitation in her voice."

"The goblin replied quickly and didn't seem to waste any time coming up with excuses."

You can also play with the character's perspective:

"You were too distracted by noise from outside to make a good read on her."

"Evidently you were staring at something other than his or her face!"

Insight, Perception, and Stealth, are problematic skills, as there's often a gap between what the Character perceives or believes, and what the Player sees on the die roll.

There's another way to handle it, which is cleaner - but not all Players will like it, so you'll need to judge whether or not it fits your table.

Insight, Perception, and Stealth are eliminated as Player skill rolls. Instead they become the targets for NPCs rolls on Deception, Stealth, or Perception respectively.

• Player: "Does he seem on the level?"
• DM ( rolls a d20 )  - "He's telling the truth".

Note that from the outside, we can't tell if the NPC is lying and is just good enough to overcome the Character's Insight score - or if the NPC is really telling the truth. A clever DM would roll in either case. Also a clever DM will describe what the Character believes as an absolute truth.

What might really be going on, is as follows:

• Player: "Does he seem on the level?"
• DM ( knowing that the NPC is lying rolls Deception for the NPC, and compares it against the "passive Insight" of the PC ) - "He's telling the truth".

Or

• Player: "Does he seem on the level?"
• DM ( knowing that the NPC is telling the truth  rolls a dummy d20 )- "He's telling the truth".

This removes the disconnect between what the Character believes and what the Player sees on the dice roll, but as clean as it might be, many Players will not like it because it takes a die roll out of their hands - and Players like rolling dice, and feeling as if the responsibility for success/failure is in their hands ( even if the mathematical probabilities are the same ).

If your Players start "dog piling" with "Do I think he's telling the truth?", well ... his Deception roll has already been made, and can be compared against anyone's passive Insight scores. You can still just tell them yes or no, accordingly - no more rolling needed.