Mental Checklist for Tactics Trainer?

I have some things I've done and currently do.

One is at the beginning, go to each of your rooks, bishops, and queen and trace the lines of movement with your eyes all the way to the edge of the board. So you'll notice that your e1 rook is looking at the e8 king even if it's through 4 pieces. Or if there is a bishop on a1 you wont miss that it's there.

Then find every move of yours that is a check, no matter how suicidal. Every move that threatens a queen, every move that threatens a rook, every move that threatens an undefended piece, and every capture you can play.

After that, you should have some ideas for a solution. Solutions to puzzles are always forcing moves, so you need to find these moves. Then you calculate.

If one sequence of threats doesn't work, try it in a different move order. If you captured with the knight first, calculate capturing with your rook first instead. If you checked before the threat, try it the other way around, etc.

To test if your move is really a threat, pretend you get to move again. Can you actually win something? Or were you relying on them playing a capture or recapture?

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When looking for your opponents best defense, find their checks and all the ways they can threaten one of your rooks or queen. In a puzzle if you see they are threatening mate in 1 to your king, then that's a big clue... every one of your moves has to be a check.

Other than responding to your threat with a bigger threat, there are 4 basic ways for them to react to your threat:
Capture one of the attacking pieces
Add a defender to the threatened piece or square
Move a piece away from the threat
Interfere with the line of attack (if Re1 checks king on e8, they might move a piece in between for example).

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This is a lot to keep track of at first of course, but as you get better more and more of it becomes automatic. To start I would at least trace the lines with my eyes and find all the checks. Then start calculating captures.

And unless you're spending 10 minutes per puzzle, I would just ignore the timer for now until you get some of this into being a habit.

Of course it helps to be familiar with what the basic tactical patterns are:

Fork, pin/skewer, removing the defender, discovered attack/check.

Some tactical theme lists are incredibly long, but these are the basics.

Don't forget Queen Sacs!

Ok, and queen sacs

Tactics Trainer is a training tool.  It's focused on pattern recognition*, and is analogous  to a text book.  First, as stated above, learn the basic tactics.  Then, try to solve the problems.  If you get the problem wrong,, don't worry about  it.  Study the solution.  If you don't understand the solution, no problem.  You will eventually be given problems that you do understand.  Then you work your way up, and eventually  you will understand the solution.  Then you will get higher level problems that you don't understand,and the process repeats.

Like all learning processes, it's slow and methodical and requires constant repetition.

*This training is not aimed at calculating moves (if I do this, my opponent does this).  It's aimed at recognizing a position (or a similar one), and remembering what worked the last time you saw the position.