This is a great question. There is not one right way to create mood in a story. Anything can really create the mood and the more creative the author is, he or she will be able to find other ways to create mood. For the reader to determine the mood, all he or she has to do is to read the details of the story. Here are some examples of what can create mood.
The setting can create mood. For instance, if it is a rainy and damp day, where the sun has not shinned in a week, these details create a certain type of mood.
The time of day can also create the mood. Something at midnight is different than something at two in the afternoon. For instance, horror books usually have actions take place in the evening.
Characters can also create mood. If the character is obviously happy, this creates a certain type of mood, one that is bright. If the character is filled with fear and anxiety, this creates a different type of mood.
These are some examples. The key is to look at the details.
I'm not a professional, but determining the mood of a story can be identified by diction and the situations that happen within the plot.