You ask if there's a routine to follow that helps one figure out the theme of a story: Not the first time you read it! That is a definite no. A story should first be experienced as a work of art. Experience the art first, look at it as a whole. Do not look at it for its parts.
That said, once you've read it once or twice and know it well, and you want or need to analyze it to see how the story works, you can look for theme. Theme is simply the ideas raised or revealed by the work of art. It is an abstract idea that emerges from a work of art. Do not look for easy one-liners that tell a reader simplistic lessons on how to live life. That kind of thing is for didactic writings--writings that attempt to teach or preach, rather than reveal. Look for ideas.
I don't really have a formula for you, although another editor might. I'll just tell you some things to look for:
- what is the subject matter? If the story is about a poor person who suffers at the hands of wealthy people, the themes are probably poverty and oppression and injustice, for instance.
- what are the images used and what do they suggest? If an image is a white, pure lamb, the theme is probably purity or innocence.
- what figurative language is used and what does it suggest? If nice church choirs are metaphorically compared to the shrieking sounds of an artillery shell coming toward helpless infantrymen, the theme is probably the horror and terror of war.
Again, I don't really have a formula for you, but I hope those suggestions will help.
I always tell my students that when they have to read a novel or story for a literature class, always have a pack of sticky notes on hand. Every time you come to something you think is profound, mark it with a sticky note because it may have something to do with the theme. Every time you tend to see objects or dialogue or events that seem to occur over and over again, mark those -- they are probably motifs, symbols and/or theme markers. For example, if you are reading Moby Dick and you keep seeing the color white appear over and over, ask yourself what the author might be trying to say. White usually means purity, but not in this novel. Also notice the characters - how are they described? Mark significant comments about them or significant things they say with a sticky note. Make sure you write on the sticky note why you marked a particular section, though, because when you get done, you don't want just a bunch of sticky notes with nothing on them -- you won't remember why you put the note there.
Don't worry so much about figuring out the theme while you are reading because it may not come together for you until the end -- but do be aware of things to mark.
Another good thing about sticky notes is that teachers usually give writing assignments on novels or short stories and they almost always ask the usual things about character development, writing style, dialogue, plot, setting, etc. So if you mark these things as you go along, it is MUCH easier to find them when you get done with the reading.
I am sure some other teachers will have other methods - you should use the one that you think will work best for you! Good luck.