This is something we spend a fair amount of time on with our students at Animation Mentor, but if I had to come up with just a few quick suggestions, they would be:
1) Write what you know. That's a big cliche for writers -- the idea that they will come up with the most genuine stories by writing about things they are familiar with from their own lives, but I think it holds true for animated short films as well. You can draw on your own experiences, your own emotions, your own stories, and then expand from there! The whole short film doesn't have to be autobiographical, you might start with a seed of truth and reality and then careen off into something wholly imagined!
2) Don't hold yourself back! If you're trying to come up with film ideas, then no idea is too silly, too difficult, or too strange. Let your mind wander, and let one idea lead you to the next, and see what crazy places your imagination might take you! Sometimes the weirdest idea can be molded into a cohesive short story that people can identify with.
3) What's your twist? Every short film doesn't HAVE to have a twist at the end, but if you're talking about a 1 minute short film, it sure doesn't hurt to give it a punchline or a twist ending. Something unexpected that sheds new light on the story, the situation, or the characters is great.
4) Pitch your story!! Don't just think about it on your own for a while and then settle on the idea. Pitch the idea to your friends, family, and colleagues and see what they have to say! If one person has a suggestion, that's all it is - just an idea or suggestion that you can take or leave. But if 3 or 4 people have the same reaction, be sure to pay close attention to what they are saying - that should be a red flag that probably needs to be addressed.
Hope that helps! Looking forward to seeing some cool new short films!