This answer will be updated as the series develops
One of the major factors that will heavily affect your solving experience is that it is difficult to visualise the moving parts. For your convenience I've made a tool that can create, visualise and simulate Square Spin puzzles. You can download it on GitHub
Now the question is "how should you solve them?". Well, here is a list of the do's and don'ts and what you should generally expect in the process.
1. Keep the true goal in mind
The main goal is to find out the minimum number of moves required to change one image into another. There isn't much point in "finding a solution" if the solution you find doesn't contribute anything towards the actual solution. It is for this reason that your initial concern should be in the number of moves and not how you reach that number. An approximation based on the parts present in the puzzle is a great way to start off!
2. Closely follow the rules
The rules are very important. They will play a large role in the puzzle and a good awareness of them can help to rule out most dead ends. It is highly likely that the puzzle in question takes a unique spin on at least one of the rules so it is important that you keep track of what is possible within the rules.
3. Guesswork doesn't work
These puzzles are designed so that it is possible to logically deduce the answer from the information present, guesswork is a waste of time. If you use the correct logical reasoning at the right time then these puzzles become very simple. Also there is a difference between guesswork and educated guesses.
4. Ambiguity is everything and nothing at the same time
It may seem that information has been lost to the void due to ambiguity however a lot can be gained by looking at the final image, don't just rely on the initial image.
5. It's how it got there, not what got there
Well this is a bit of a strange one but even although you have to keep in mind that a square in the final image can be of many types and of many origins, it is more important to realise that however it got there - it most likely got there in the fewest moves possible. You can use this information to work backwards and find the potential origin. In doing so, you may discover the mechanism responsible.
6. Choke on your food
The more you do at once - the better. Moving the most amount of squares in a single move is more valuable than many individual moves. Setting up for a large spin conserves more moves than you think...
7. Mechanism awareness
Knowledge of previous square configurations will be helpful in the long run. Some configurations will commonly appear and knowing what to expect matters.
8. Useful vs useless perspective
It is important to distinguish between what squares will greatly affect the progression of the puzzle and what squares are redundant to consider. For example, in this puzzle only the movement of the red squares matters and it would make no sense to instead consider the whites as there are more whites than reds and they are both linked anyway.
9. Keep it simple
Overcomplicating things may inflate the number of moves. There is a logical way to go about it, a messy solution is a red flag.
10. Unmovable squares (Un) aren't exactly invisible in the problem
You may be tempted to dismiss Un squares as "simply not apart of the grid" which can be a good approach however you need to remember that just like the theoretical squares outside the grid - it isn't possible to contain it in a spin. They also can be spun if they are in the exact middle of the area being spun. Hmm...