My answer deals with visualization and is mostly taken from Jon Tisdall's book Improve Your Chess Now.
Using a puzzle or game score, visualize as many moves ahead as you can comfortably manage. Go slowly, and after each move visualize the new position and look around the board. What squares are newly attacked? What files have been opened? etc.
When you start to feel you're losing track of the position, stop calculating and remind yourself where each piece is by looking around the board. Do this until you can quickly recall where they all are. Basically you will memorize the position. After that try to go a few more moves. If you lose track, you can go back to the memorized position and try again.
After it's over I think it's useful to now move the pieces. Check to see if the positions you very clearly visualized were correct. Were you right? Where they any open files or newly attacked squares that surprise you now that you can move the pieces? Think about ways you might avoid those mistakes in the future.
I did this every day for about a month while solving tactic puzzles and my visualization improved a lot. But it does take practice. If you stop playing or training for a while you will be rusty.
Do I have to solve chess tactic puzzles until I can solve difficult problems?
Or does anyone has his/her own training method?
Thank you for any advice.