How would one discover this tactic...?

I thought I had a really strong thought process/algorithm for finding tactics, but this was the first "simple" (as in short, move-wise) tactic I've seen that's been an exception to my thinking algorithm.

How would one see this tactic in a real game, say a classical game, and not knowing that there was a win?

Try solving it yourself - the solution is as short as (3 moves), but nowhere near as easy as the mate in 3 that someone else posted a while ago, when asking how to find a tactic. The first move isn't hard, but the second is very unnatural looking, instinctively, which makes the third rather obvious. 

The answer is somewhere below in white, so just highlight to see the solution. 

1...f5 2.d3 Be6 3.dxe4 Bc4 and white has nothing better than to give up an exchange for no compensation.

It seems like considering forcing moves blindly would not even work here, since the surprising move in the combination is not forcing in any way, and only by trying to take advantage of some irrelevant tactical motifs can black even try to find the solution.

You would need to consider forcing moves blindly *and* just keep calculating when your mind tell you to stop. 

Intuition, because generally humans don't play like computers.

I didn't solve it... but I was looking for a tactic. There is no tactic. The tactic only happens after white tries to win the knight. This is a position which I might solve in a real game, but telling me it's a tactic makes me go about it in the wrong way. This might be related to why your method didn't find this solution.

You mention calculating even after you'd normally stop. This ability, or aspect of analysis, I think is called fantasy. Asking "what if I move . . . " and then keep calculating even if the move looks bad to see if you find anything.

As for a method to solve this, when I'm desperate to find something in the position I look for exactly what's changing. If I'm calculating d3 and dxe for white, then I look at everything those two pawn moves change. It removes a defender from the knight, it opens the d file, and it also opens the f1-a6 diagonal. Once you notice that diagonal, you'll probably also notice the queen and rook are lined up. (It also closes the 3rd, then 4th ranks. As you might imagine trying to detail the geometry in a more complex position can be challenging.)

Although in a real game, since black is a piece up in that position, I don't think many players would be desperate. They'd probably castle without much thought.

The "tactic": White is going to win back the piece sacrificed, and all lines lead to an about equal position, except for the 3 moves I showed (where each move by black is forced for the advantage, and each of white's moves are the single "challenging" move in the position); if white doesn't play d3, black keeps a full extra piece, and is winning.

In a real game, I'd probably do ...f5 without thinking of the followup or ...Bf5+0-0-0, which does look good, but misses the nice tactic. 

I didn't like ...Bf5 because you're just getting kicked when the knight is captured.

Better to do something like ...f5 d3 Be6 dxe 0-0-0 if you want to move the bishop and castle to that side.

The solution is very computer-like though. Maybe a better way to present the puzzle is to say something like:
"In the game after 1...f5 2.d3 0-0 3.dxe fxe 4.Qxe4 white was a pawn up. What did both players miss?" (stealing this from a puzzle book I have). That way the solver, just like in the game, starts with a principal variation, then they try to improve it.

It is very computer like. One of my dreams in chess is to be able to find and play these computer-like lines, and foresee them, like before playing 1...f5. 

If I could find these short computer-like sequences as quickly as I find "normal" short tactics, that alone would easily give me hundreds of points. However, doing so *without knowing* there's a tactic there seems almost impossible, while keeping the clock in check.

This, and the fact I missed a mate in 3 recently, shows I need to work harder on my tactics/calculation.

Highlight the white space in post #1 for the 3-move sequence, which starts with 1...f5.

This is the "elegant" side of raw tactics. Show beginners this kind of stuff before showing them Karpov's beautiful positional grinds, and maybe it would encourage beginners to not drop pieces before trying to do advanced positional play. 

Well then, the answer is: 1...f5 2.d3 (the only challenging move, or else black is up a piece) Be6! (breaking the pin, so..) 3.dxe4 Bc4! and black wins an exchange, since the bishop is immune, and the queen doesn't have any threatening squares to go to. 

The only line that gives black a clear advantage. Unfortunately, I'd probably miss this even in a classical game... maybe if I got lucky enough to play 1...f5 over 1...Bf5.

I may have thought to play f5 if I was playing, however, I do not believe I would have thought of the next Be6 then later Bc4!  If I would have got lucky enough to just merely push my wood onto Be3 I maybe would have seen Bc4, but only MAYBE.  There are a lot of maybe's in the equation though, so it might probably never would have happened in an actual game where I made these moves.

This is just incredible, Cherub!

Of course I failed to find it. 

It's not simple at all. 

The forced move is there - of course - but you need an in-between move to bring it about. 

Ask yourself - "I now have a free move until white takes my piece. What can I do during this free move that will inflict the utmost PAIN"? :-)

And all this when your experience screams at you to CASTLE already - the enemy is developed, there's a QUEEN in front of our king - 

And no. We find time for a quiet manoeuvre, IN THE FACE of a discovered check - and against every possible indication (the uncastled king, the discovery, the anti-positional nature of ...f5 before castling) - yet the tactic works. 

So yes, quite impossible for this modest poster.

I saw a tactic similar to this... I wish I had saved it. Out of a totally bland looking position there's 2 ridiculous moves, but then "magically" everything works and you win a piece. Of course the engine found it for me.

I asked a GM what level of player would you expect to see this? Would a master see it? He said no, I don't think so, but a GM would. I asked how. He said you consider a wide range of candidates and always look for forcing moves even if at first it looks bad.

Maybe not very helpful, but seemed related.