Generally, stories are written in the past tense.
The present tense is used to give a sense of 'immediacy' ... so that the reader feels it is actually happening right there and then. (Or here and now?)
For an example of how tenses can be mixed to give this effect, see 'Next Summer, Riyadh?' by The English Master.
Present tense also works well if the story is told in first person, especially the 'stream of consciousness' type of story. My own, 'Important Contact' I offer as an example.
Past tense is the norm, and, I think, the easiest to work with, but it's worth experimenting as the effects can be rewarding.
(I not only stayed conscious, I LOVED grammar! Noun, singular, common, subjective. Verb, active, past tense ... sorry!)
