My best way might not be best for you. Might not be best for Gerald also.
[Who is Gerald? Anybody not you and not me.]
My best way may not even be considered as best even by me.
Say there is really a standard best way and it is taught in classes, or is kept secret but is known all over the world due to the Internet. Say also almost all of the students can follow that best way. Wow, what a wonderful world it will be as far as solving word problems is concerned.
No, there is no best way. Good ways, various of them, yes, there are.
Here is a part of a good way, my style. It may not be good for you or for others, but, hey, it works for me.
Read the word problem correctly. Find what is being asked for. Understand what is being asked for. Because the solution revolves around that what is being asked for.
List down the givens. Or be aware of them. Are they related to what is being asked for? Are they related to each other, or one to another, to create a relation to the what is being asked for with that/those relations?
Make relations about the givens and the what is being asked for in the forms of equations or proportions or functions or whatever, any relation. Then work on those relations to find what is being asked for. [Relations by formulas, guesses, sequences, whatever.]
Is that a good way for you?
Oh, I always say, if you know what is being asked for, then you solved 30 percent of the word problem. The other 70 percent may only be "mechanical" or "following the flow"---the "dirty job", yes, but in many times easy only because you have or you know the "goal".
(2) Why do textbooks call word problems APPLICATIONS?
I don't know. Our textbooks when I was going to school called them word problems.
"Applications" by others maybe because the word problems mostly deal with actual, concrete, physical, real life situations. Have you heard about Applied Math? Why "applied" math?
(3) Why do elementary school teachers call word problems MATH STORIES?
Again, I don't know. Our teachers then called them word problems.
(It was simpler then.)
Word problems. Words. Stories.
"x^2 -3y = 4" is not story.
"If three times a quantity is taken away from another quantity that was multiplied by itself before, we get four items." Sounds a story to me.