If you're not already, get good at K+Q vs. K. Then play Q vs. N as if the knight weren't there, except don't hang the queen or allow a fork.
Queen Vs. Knight Checkmate

Thanks n9531l. I am fine with K+Q. I will give it a try.
Edit: I have tried as you suggested but seems that K+Q Vs. K theory is difficult or impossible to implement here because of the Knight . Isn't there anything else that I should know or keep in mind for this K+Q Vs. K+N checkmate?

Well, post a position where you think the Q vs. N mate is hard to figure out, and let's see if my suggestion is any help.

To answer the question though, the method is to activate the pieces, get the K onto the edge, then separate the K from N by using zugzwang motifs.
That's the scheme, but it takes practice/planning to pull it off.

I went to V3 to find this position, but failed. I did find the "Drills" section, but not this puzzle. Where exactly is it?

Don't you find 'Drill' under 'Learn' menu? well I think, I should insert a screen shot.
You should find it now easily
EDIT: oh wait, I think this particular drill is under premium membership feature then.

it's under the 'Checkmate' sub-section and there is only one page in that sub-section. Just wait, i will add another screen shot for you.

Ok, my method was by no means best, but you can see that what I did was strive to activate my king, drive Black's K onto the edge, then separate the K from the N.

Here's a faster method:
1.Qc3Nf5
2.Kb5Nd4+
3.Kb6Ne6
4.Qf6Nd4
5.Qf4Ne6
6.Qf5+Kd6
7.Qe4Ke7
8.Kc6Kf6
9.Kd6Ng5
10.Qf4+Kg6
11.Ke7Nh3
12.Qf3Kg5
13.Qxh3Kf4
14.Ke6Ke4
15.Qc3Kf4
16.Qd3Kg4
17.Qe3Kh5
18.Kf5Kh4
19.Qc3Kh5
20.Qh8#1-0

hey SmyslovFan, tell me something. In the 2nd repertoire you posted, after 11...Nh3, why didn't you play 12.Qg4+? That would have won the knight on the very next move either on h3 or on g5 depending upon black's move. Am I missing something?
Edit: Sorry, I messed it up, never mind.

@Subha_Learning: If you want to practice with this position, we can play it out. I'll tell you what I would play as White and why, and you'll give what you think is Black's best defensive move.
If the knight were missing, I would start with Qe3 to confine the black king to the area where my king is. So I'll check to be sure I'm not giving my queen away to a knight capture or fork, and make that move, 1.Qe3. Your turn.
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I am stuck with Queen Vs. Knight checkmate. Despite of trying so many times, I failed to chalk out a plan for the checkmate. I would like to know the theory or pattern that can guide my moves for the checkmate. Please help me out.
Thanks