Social interactions are often an interesting challenge. It's a mix of solving a puzzle and telling a story.
To help solve the puzzle, I find it helps me to ask a couple questions to the DM: Do I notice anything odd about the NPC? Is he holding a weapon or is he unarmed? What kind of body language does she have? Does she seem aggressive, angry, confused, nervous, or calm? Is he fidgeting, sweating, avoiding eye contact, or anything unusual that makes me think he's lying? If there's a group: Do the other NPCs seem to be in agreement with the leader? Do I notice any signs of anger or contempt from any of her followers when she says this? Is anyone in the group trying to catch our eye, or trying to secretly communicate with our group? Don't ask too many questions, but a couple key questions can really help out a lot, especially if you're confused about what to do or say.
Now keep in mind the DM may have to come up with a lot of this on the fly, and there may not always be a clue for the scenario. But asking questions can help prompt the DM to flesh out the character, think about their motivations, or drop a clue for you. This kind of back and forth can be really rewarding. It lets you make some progress in understanding the situation, and it gives the DM an opportunity to flesh out the scene and add some more depth to the NPCs.
And to help tell the story, take a look at your character. Look at your personality, ideals, bonds, and flaws, as well as any other quirks you've come up with for your character. These are your guideposts. Try to flavor your social encounters with these "abilities." What is your goal for this encounter? Always keep in the back of your mind what your character wants. This is his story, and he should be trying to fill his bucket list. You don't have to overdo it, but it helps to know what types of actions you'd be ok with, where your loyalties lie, and what you want to accomplish.
Note: while it's important to think of your goals and motivations, don't overdo it. Don't spend a week at the library instead of going to the dungeon just because you have a sage background. You're an adventurer, so your primary motivation is to explore, find treasure, and go out and adventure. Ideally, everyone in the party should try to be proactive and build on each others' success; not go off and do their own thing. The game works so much better when everyone is working together towards a common goal; you'll have individual goals, but you certainly shouldn't forget the team goals.