In order to attack the enemy King, we must learn to SEE the LoA landscape (lines of attack).
A mate is most of the time delivered by a Queen, on a square nearby the enemy King. Assisted by a piece of some sort.
The square on which the Queen delivers mate, is called the focal point. Let's not be bothered by semantics, I like the term, and it is more commonly known than PoP (point of pressure).
From the focal point we trace back to the attackers, which delivers us the LoA's. A LoA is the line of attack from attacker to the focal point. It consists of ranks, files, diagonals and crooked lines (for the knight). The LoA can contain pivotal points, where the line of attack changes from direction. We need to know how many attackers can be added to the attack, and how many tempi they need to reach the focal point.
Further we need to SEE what de defenders are. The defenders can interfere with the LoA's or the focal point.

Diagram 1. White to move 
r3r1k1/1qp1bppp/p2pb3/1p5N/4P3/P2Q3P/1PP2PP1/R1BR2K1 w   0 1
The focal point is g7.
The first question is: if black was not allowed to move, how many tempi would it take white to mate? The answer is two tempi. 1.Qg3 . . . 2. Qg7# or 1.Qc3 . . . 2. Qg7# or 1.Qd4 . . . 2. Qg7#
Let us let have a look at the relevant LoA's.

Diagram 2. Showing the LoA's 
We talked a lot about postponement moves in the past. Moves that postponed the mate, but didn't alter the final outcome. They usually come in series of two plies at the time (action and reaction).
It is easy to see, that we only need to worry about defenders that can interfere with the LoA's. If black moves with the rook to Rb7, it doesn't have an effect on the LoA's. So we can happily prune the tree of analysis by ignoring the rook on a8. All moves that are irrelevant to the LoA's can be ignored (unless they can threaten our King). Can you SEE how this prunes the tree of analysis?
Which defenders can interfere with the LoA's? I reckon the focal point to be a part of the LoA's:
A move like Bg4 is a typical postponement move.
1.Qg3 Bg4 2.Qxg4 has no effect on the final result.
The reason that Bg4 is such a feeble move, is that the light squared bishop acts alone. If you have a look at the LoA's, you can SEE that there are already defenders that interfere with the LoA's ON THIS VERY MOMENT.
already cover a square on one or more LoA's. We must look for two defenders that both cover the same squares of a LoA. Which squares are we talking about?
 f7 is covered by Be7 and g7
 g6 is covered by f7 and h7
 g7 is covered by the King and potentially the dark squared bishop
We only have to worry about these squares and their defenders. Can you SEE how this prunes the tree of analysis?
The next question is: how can we UNDERMINE the defenders of these squares?
The global answer is: by adding attackers. We can add Bc1 and Rd1 to the equation. Can you help to finish the story?
To be continued. . .
UPDATE Dec 13th
To gather more information about the scenarios that play a role in the realm of the lines of attack, we must have a closer look at how the defenders can interfere with the LoA's. We can do that best by having a separate look at the two LoA's that involve the queen.
Blockading the LoA with a protected piece

Diagram 3. White to move. Protected pawn blocks the gfile 

Diagram 4. White to move. Protected pawn blocks the gfile 
Adding defender to a piece that already blocks the LoA

Diagram 5. White to move. Black added a defender to g7 
Now let us investigate the other line of attack of the Queen.

Diagram 6. White to move. f6 blocks the LoA and is double protected 

Diagram 7. White to move. Black added a defender to g7 
As you can see, g7 plays a crucial role in blockading both lines of attack. You need the knight and the Queen for to deliver mate. So you must look for other attackers to undermine g7.

Diagram 8. Black to move after 1. Bh6. Underminding the defender g7 
The most dangerous answer of black that must be investigated first, is taking with the g pawn on h6. If you don't know how to follow up, you are basically lost with a piece less.
To be continued. . .
UPDATE Dec 14th
As you can see, after 1.Bh6 gxh6 black has created a new defensive square on g5. The defense against the LoA along the gfile is reinforced, but the defense of the diagonal c3g7 is weakened.

Diagram 9. White to move. 
After 1.Bh6 gxh6 2.Qc3 you notice that the f6 square is weakened. If f6 is played, it denies the bishop access to g5, so the gfile is open again.

Diagram 10. Black to move 
The only thing black can do now is to sacrifice Be6 on the LoA , and after 4. ... Bg4 5. Qxg4+ black has created an escape square on e6 for his King with tempo at the cost of his bishop.
Can you see how all logic revolves around the lines of attack? Can you see how this prunes the tree of analysis, making it more manageable and calculatable?
This is the way I'm going to analyse the positions in the Art of Attack in Chess. Thus hopefully absorbing the chess patterns that belong to the "LoALogic".
Game 2:
Overall question: At what point(s) did you feel like you had no plan or even an idea of how to proceed? After move 57. It were the last 5 minutes and I didn't need to write the moves anymore. I totally outplayed him in 5 hours. This is what Stockfish thinks: