I like a bishop on d3 for that kind of thing.
How Do You See This Tactic?

This is actually a very common idea in the Caro-Kann and some Sicilian lines (sacs on e6 in sicilians are pretty typical).
Your thinking algorithm should include all forcing moves, no matter how ridiculous they look at first, to be candidate moves. All captures, checks, and threats should be candidates. If they work, they almost always win, and if they fail, it's usually obvious within a few seconds.
So it's (1) pattern recognition and (2) thinking process that weren't good enough for you to not see this tactic. Since you'll always be missing some patterns in your recognition, you need a good thinking process to find winning moves anyways.
In terms of creating a thinking process that can detect all tactics, this tactic really, tbh, isn't very challenging. There are some tactical moves that you would think a player would find only by pure luck. For a start, check out Chess Mentor's "Advanced Tactics" - the first one alone is beautiful, but pretty tough to spot, because it looks so strange. Note that, if you actually looked at all forcing moves, you would be able to find that tactic , because it threatens a mate in 1, although very blatantly.
Yeah that's pretty easy. Train your mind to look at all forcing moves no matter how absurd they look at first glance.

I saw it in about 5 seconds. Start doing tactical exercises every day....it goes a long way towards increasing your tactical vision. Playing aggressive openings can also help you improve your tactics at a faster rate. Always calculate forcing moves first...often times tactics present themselves in forcing sequences.
You need to have learned the pattern before to see it immediately. A good chess tactics book will teach you the patterns and then show you a bunch of examples.

No idea what that picture is from or what it means, but I was being serious , assuming you saw that tactic.

I think the advice by IM David Pruess about learning tactical patterns is helpful. See Post #35 in the thread https://www.chess.com/forum/view/general/chess-advice-most-chess-players-dont-like-to-hear?page=2 . If you do so, you will solve this kind of tactic in a few seconds just by seeing the pattern.

I found the OP's puzzle to be a tricky one, too. After 1-2 minutes I still didn't see the solution. After your hint about the e-file I even considered the correct queen sacrifice, but I simply failed to notice the subsequent exposure of f7 combined with an outposted knight and bishop ready to check across the f7-square. However, I don't play conventional Sicilian or Caro-Kann lines, so I'm unfamiliar with the typical tactics of such positions, and often my positional knowledge of openings I do play is what saves me, often by increasing my sensitivity for certain common themes in those openings.
I'll post it as a puzzle in case anyone wants to solve it. I don't know how I would see something like this. I stared at the board for over a minute and didn't see anything at all. I noticed the queen on the e-line sure but that was it...