I promised the students that I would post some links to short story outlets on my blog so here they are:
1. Laura Hird's website has a lot of useful information on short stories and I think she has a competition most months;
2. The SEED Magazine in the US currently wants short stories of less than 4 000 words by March 15th;
3. East of the Web takes short story submissions;
4 ...and the Barcelona Review.
I am sure there are other websites offering publication of short stories.
Then there are magazines such as the People's Friend and Mslexia which cater to different tastes. Mslexia only takes pieces from women and I don't think they pay. In all cases the standard advice is to read examples to assess house style and to see if it matches your own - but I am sure you know that already.
Then there are prestigious competitions like Bridport and many other national and more local competitions, most of which require a fee to enter.
Jason Erik Lundberg's latest podcast has excellent advice on submitting short stories to an editor as well as important information on how to properly eat chocolate.