Pick up any issue of Writing Magazine, but especially this one, and you will find dozens of short story competitions. If you are keen to hone your craft they provide good practice with working to a deadline. Even if you don’t win, you may learn something (particularly from those that offer critiques) that will put you amongst the winners next time.
The following points are aimed at helping you towards success. If possible, allow plenty of time so that you aren’t doing things in a rush.