There's a bundle of things you can do. As I was writing to a 2500-word limit, I settled on in media res, where the story starts part-way through. It stops you waffling, and you can also selectively reveal backstory through flashbacks, which is really useful if you want to keep your readers on edge.
Basically, if you don't know where to start, work with what I call the What If Scenario, and it's used by a lot of authors. In short, ask yourself "What if this happened?". In my case, I asked "What if I completely removed the main character's ability to speak?". When I decided I liked that, I asked myself "Alright, why can't she speak?" and I went and looked up causes of such a condition and settled on an extreme case Post-Traumatic Stress Disorder.
You're only really limited by your own creativity, but remember that short stores tend to centre around events and longer ones around the characters. Make your characters interesting (there's nothing I hate more than stories with bland people in them). Don't describe them physically, but use their personality to paint their portrait. The reader will gain an idea of what they look like, and if you do it right - and it can be very difficult - two readers will get the same idea about your characters.
Look to the people you know for inspiration. Everybody has a personality, so take traits from two or three people, combine them into one cahracter and start exaggerating and downplaying individual parts. Don't say "John Smith is 123 Generic Street was an arrogant bastard" when there really is a John Smith of that address with those tendencies. I'll take myself as an example. Normally, I'm a bit of a smart-arse and a little jaded with a tendency to have to sole every puzzle I come across. That's a very simplified desciption, but when I touch it up, I become the gentleman's Han Solo. Just watch a few people, how they act, how they talk. Don't ask them about it, but just watch. Splice them together and tinker a little and you'll get someone very interesting every time.
I don't know what your word limit is - I never did EE2, but I've been writing for as long as I can remember - but don't be afraid to describe things. If you have a word count of 10,000, then write 9,750 words or more. Try to add an extra dimension to your work, but don't go overboard. We always try to solve the little puzzles because we can't solve the larger ones. Your characters won't always have the answer. They'll screw up, and they'll make mistakes. No-one is perfect and as an author, the aim of the game is to make characters who are as real as possible.