The first area of attention is the killbox. Is there already a killbox, or must you erect the walls first? Is the king already in the killbox, or must you chase him into it? Have you already access to the killbox or must you pry it open with a sacrifice first?
All normal tactics can play a role. Like double attack, discovered attack, clearance, pin, blockade, lure, magnet et cetera.
Tempo moves are extremely important. 80% are checks, the rest mostly threatening mate in one. Capture is irrelevant.
What patterns and logic plays a role with a killbox?
A few examples
|Diagram 1. Black to move. Mate in 3|
6k1/1p4n1/8/2RPQ3/4p3/P3qbP1/7K/2R5 b - - 1 1
Here you must divide the killzone first. The white king must decide in which killbox he wants to be mated. The black queen must split the killzone by a double attack, where the double attack means delivering mate in killbox 1 or in killbox 2. This splitting is a common theme.
|Diagram 2. Black to move. Mate in 3|
3r2k1/2p2pb1/1p1r3p/p5p1/P3P3/1P2NnPq/QB3PN1/3RRK2 b - - 0 1
Another common theme is to cover the escape square. At all costs, in this case.
|Diagram 3. White to move. Mate in 3|
r4k2/4p3/5NpN/1bp1Q3/P7/7P/1P4PK/3q4 w - - 1 2
Another common theme. The white king is in the killbox, but there is no adequate check to deliver mate. A common tactic as a discovered attack adds a duplo threat to the equation.
|Diagram 4. Black to move. Mate in 3|
6k1/p1p2Rbp/b6q/2pBP3/2P3Q1/P5P1/1r1n3P/6K1 b - - 0 1
There is no killbox yet. The queen sac serves only one purpose: that the next move can be done with double check. The tempo battle is extremely important, and a recurring theme in every mate.
|Diagram 5. White to move. Mate in 3|
2r1k3/2q5/p1rbp1R1/2pp3Q/1P1P1P2/P3P3/7P/2R3K1 w - - 0 2
Here you must erect the walls of the killbox first. You do that with a discovered attack. The second goal is to chase the king away from the point of pressure f8.
You see, it is not exactly rocket science. When you work your way through a themed database of 250 mates, you start to see the common logic.