What are the necessary steps for solving any puzzle?
It depends on what kind of puzzle it is. Sometimes you just have to consider all the facts and make a deduction. The facts will be given to you and you just have to connect them in the right way.
Then there are open-ended puzzles, like those puzzles about graph theory(you've probably seen them). In these puzzles what you have to do is just to investigate. You usually will not be able to tackle the big problem all at once, so try to simplify the question a little bit and work on that version of the question instead. If you can not find a way to simplify it, just play with the puzzle. Do anything you like, as long as it is about the puzzle at your hands. It will not always lead to a solution but you will have more information about the puzzle, making it easier for you to reach to an answer.
But, at the end of the day, it is up to you to solve a puzzle. The "step"s I provided are very broad. I can tell you this though: Be stubborn. There were a lot of puzzles where I thought it was impossible for someone like me to find a solution. Even though some of them took days to solve, I did solve them.
I am no expert though. I might be giving wrong advice here. I am just sharing what I learned through my own experiences and what worked for me.