Over the many years of my life I've developed a number of different ways to think. That might sound strange, but you probably have a few ways too, ones that work for you in different situations. I've found that writing my list down makes it easier to remember to apply them in a much less random fashion. So here's my list, for whatever purpose these might be useful to you.
Of course, there is just Basic Logic. Apply what you know, take it step by step and reach whatever conclusion those facts and steps lead you. Works for most the daily details we deal with, but is amazingly counterproductive, or at best useless, for anything other than these rote tasks.
A useful inversion of Basic Logic is Working Backwards. Start with the goal you want to reach and then work the problem backwards. Find what has to happen just before the final result is reached. Then repeat that backwards process until you reach where you are today. While I use this in many situations, it's particularly useful in solving mazes, those little box puzzles where you have to draw a path from an opening on the outside to a destination somewhere inside. While the same path must eventually be found, starting at the destination leaves you with fewer initial moves than starting on the outside. I solve puzzles ten times faster Working Backwards.
Abstraction strips away a lot of the details that can clog up the thought process. Take your particular situation and simplify it by changing specifics to relevant generalizations. For example, instead of "I need a flash drive to copy files to another PC", change it to "another PC needs access to these files". The first is a specific solution to the more abstract requirement of the second statement. But there are many solutions to the second, some of which might be far more effective than using a flash drive.
Another one that works for me is Under Pressure. It's amazing how many times I've either had someone say "that can't be done" or offer a substandard or unworkable solution. My brain usually ignites in these situations and an answer or a better way immediately jumps into my head. I've also had "those days" where I worked all day long without an solution only to have one present itself close to 5:00 p.m. I seem to get smarter as the working day comes to a close.
Somewhat similar to this is a Couple Seconds. I limit the amount of time I'm going to spend looking for a solution to a Couple Seconds. If a solution doesn't immediately and magically appear, the problem gets pushed to the back burner for an hour or more. Let the unconscious mull it over for awhile longer.
Extra Oxygen seems to help. I’ve developed the habit of queuing up three thorny problems at the start of a solitary ten mile run. After the first few minutes, when my pace is established and my breathing is regular, I begin thinking on the first issue. Within minutes I reach new insights and have a path of action ready to go. Then on to the next problem.Within thirty to forty minutes the queue is exhausted, which is a good thing because I begin getting dis-interested in thinking and just want to enjoy the run.
Green Hat is part of the six hats method I learned at work. During a group Green Hat session, no one is allowed to offer any criticism or objection to anyone's ideas, but they can offer improvements or spin offs. Keeps the creative juices going when you don't have to worry about offering up a really dumb idea. And frequently a dumb idea sparks a less dumb idea that eventually ends up being a really great idea.