The Business End
For those of us who like to write, that's the easy part. The hard part comes afterward--where to flog your work, when's the best time, who's reliable or not?
Short story contests run throughout the year but mainly look on the Net for listings from September through Spring as there doesn't seem to be as much out there in the summer months. Know whether magazines are quarterly or biannual and check out submission times for same if you're interested in specific ones . If you're looking for an anthology or novel , longer works that require more editing , you will often find request for submissions by April so that publishing can go forward by November in time for the Christmas market.
Be aware that some contests are money grabs so try to discover if legitimate or not by looking at previous works, winners lists etc. Stay away from publishing that has 'pre-orders' in the contest description or trys to put a code on your work (signalling that friends and family need to 'vote' for your submission through purchase). Any market is a minefield, and the writing universe is no different. Keep your wits about you :)
Just do the research. It's dry work but unless you're self publishing, a necessity.