I recommend Timothy Hickson's book On Writing and Worldbuilding. In there he talks about a lot of topics dealing with Worldbuilding and one of them is when to exposition. I'll try summing up the sections here but I would definitely recommend you to check that book out, it helped me a great deal with the story I'm writing right now. Beware, for there are spoilers lying in the light.
Mystery: An example of this is in
Harry Potter and the Philosopher's Stone in the prologue chapter. Mystery exposition here includes the fact that Lily and James are dead but their son survives.
Emotionalism: In
A Dance With Dragons, when a skin-changer character called Varamyr is introduced in the prologue and the things about him like his personality, his traits, his desires and his motivations are revealed by R.R. Martin to the reader. This character isn't entirely off-putting to the entire story though, because as we learn more about his skin-changing ability we get to learn more about how that'll affect Bran who up until then hadn't really used his power as much and thus we knew almost nothing about it.
Techniques you go to perhaps not make exposition feel info-dumpy:
1) Narrative Perspective: Character not knowing something all the other characters already know. I use this technique in my first chapter when Bhagat asks Gahkhar why the Afraris were able to crush their rebellion so quickly. I do have to admit; however, that I hate that exchange and I do not recommend using this technique at all because it's pretty lazy unless under specific circumstances such as the character being forgetful or too tired to rationally think or maybe he's pretty drunk or high or other.
2) Narrative Payoff: You can see this in The Matrix as an example. Narrative payoff refers to the MC having to overcome obstacles to get to know information, usually the truth. Neo spends time trying to investigate a curious mystery while having to make an escape, having to be interrogated by agents and then having to get a tracker removed all in order for him to finally meet Morpheus. This usually gives the reader satisfaction that they
finally have found the
truth so it makes it feel less like an info-dump per say.
3) Pope in the Pool: Where dull information is delivered in a shocking, dramatic or humorous scene. I guess to hide the fact that otherwise, the information might turn off the reader.
4) Characterization: Really depends on the POV with this one. First-person or third-person limited will have a better time with characterisation to show the emotional state of a character. Third-person omniscient might have a harder time.
Harry Potter and the Philosopher's Stone does a great job of introducing characters in the first few chapters. This is especially true when Harry is first introduced to the reader.
5) Conflict: I use this in Chapters 5 and 7 when Bhagat fights Zander. You have to build up a fight scene or a sense of conflict between two characters and then plant some exposition during their interactions. For mine, it was when Zander called upon his Crest in the middle of the conflict to bash Bhagat into a tree.
6) Environmental: This is basically central to the idea of "show don't tell." Show what the character sees, not what the narrator says. An example of this is the movie Dunkirk when all those Allied troops are trying to flee the beach before getting killed by Germans.
7) Motivational: Used when we don't have much of a back-story for a character in the main narrative. An example is Zuko from The Last Airbender, where we see flashbacks to his banishment. This is pretty important because it gives us a clue as to why he wants to hunt down the Avatar so badly, it's a way for him to regain his honour.
As Kotohood mentioned, folktales can be a very good way of conveying exposition. In my story, there is an epic that legitimizes the system of Dharma that is so prevalent in the religions of the sub-continent and it's used to build conflict between the different religious groups as well as within a religious group. I also have several poems that I wrote to be sung by people in my story that conveys the geography of the sub-continent. That way it isn't the narrator blabbering, but the people in the story who are.
If there are things that are of knowledge to the people of your story but that it isn't something that the reader will have an easy time of understanding, you can make a glossary section on it. That's what I did at the recommendation of several users here on the forums. I made a section on religions where I gave enough information about a religion that otherwise would have been info-dumps in my story.
Here's the link.