The tips work for dialogues in short stories as well as novels, and perhaps they are more important in short stories because the author has to say much in a short space.
The aim of dialogue is to create emotional effect in the reader.
One of the things a writer has to learn by conscious application is to discard coherence and logic that is usually meant for non-fiction. Dialogue seems artificial when it is coherent and logical.
When writing dialogue, always remember that a character who reveals not enough reveals much.
Always check for conflict in dialogue.
Check whether the lines spoken are consistent with the character’s background.
Weed out any unnecessary words.
Loosen stiff sentences.
Check to see what is going on in between the lines: what counts in dialogue is not what is said but what is meant.
To me, the words I have bolded out, are really the most important pieces of advice. Drop in any additional tips in the comments and I’ll add it to this list and credit it to you.