The unreliable narrator is a literary device where the narrator of the story gives wrong information to the reader.
It’s a useful device, but one which must be used very carefully, lest you cheat the reader - which, as per the sacred contract, you must not do.
To use the device of the unreliable narrator, the story should really be in first person point of view. The reason for this is that if the story is told in any of the third person points of view, the narrator is assumed to be absolutely factual, and it would definitely break the sacred contract for the readers to find out later that they had been lied to.
So, given that only first person narrators can be unreliable, there are three different possibilities within that:
The first is that the narrator is deliberately lying to us. She knows the truth, but she’s telling lies. You would have to be so, so careful with this, as again, it would be cheating and breaking the sacred contract.
The second scenario is where the narrator genuinely believes she’s telling the truth, but both she, and we as the readers, are fooled. Again, it takes a lot of skill to pull this off well. In my second novel Missing Molly (originally 'Loving Lucy') I used this device, and I did so (at the risk of spoiling the story should you read it) by just presenting the evidence that the character saw, and letting both the character and the readers draw the obvious (but in this case, wrong) conclusions.
Showing-not-telling is very powerful in this situation. If you say, He was very concerned, then that’s a fact, and the reader is going to take that, and you as the writer have to stand over that. If, however, you write something like, ”Are you okay?” he asked, placing a hand gently on her shoulder, then you’re just presenting the evidence that he’s concerned. And he might well be, but he might be faking it.
The third scenario is where the narrator genuinely believes she’s telling the truth, but it’s clear to we readers that she’s wrong. For instance, she might tell us that she’s such an organised person, but yet we’re seeing the discarded clothes all over her floor, and see her searching madly for her keys behind cushions and so on.
This kind of unreliable narrator can be used very powerfully - there’s lots of scope there for both comedy and poignancy. It can take a lot of skill to successfully write this - saying one thing but making it very clear that the truth is different, so be careful with it too.
The other thing to think about when you have this kind of unreliable narrator is that the reader will think to herself, Ah, so she’s not to be trusted, and will reserve judgement on other things this narrator character tells. This can be to your advantage (as the writer) or not … so be careful.
I suggest you read The Murder of Roger Ackroyd by Agatha Christie for possibly the most amazing example of unreliable narration.
Another example is Nick in The Great Gatsby. Nick’s hero-worship of Jay Gatsby blinds him to his faults, but those faults are clear to we readers.
And finally, The Curious Incident of the Dog in the Nighttime is another good example, in this case of the third kind of unreliable narrator. The narrator is autistic, and a child, and so all his perceptions are filtered through those realities. We adults are aware of this and make allowances for this, and extrapolate the truth from that.
So, in summary, the device of the Unreliable Narrator is a very useful tool in the writer's toolbox, but one which must be used with care. It's great fun to use, though, as you carefully craft the words to fool the readers.