I suggest trying to make something with the short story genre. They are usually simple to understand, but at the same time open to interpretation, which can be good for an interesting story.
Read this:
http://en.wikipedia.org/wiki/Short_story
Basically, pick yourself a protagonist, create a personality for him/her and perhaps add another character or two. Try to keep them few though, you
probably don't want to confuse the player with over 10 names to remember.
Next, create an incident. Something that happens to make the story interesting. Perhaps something went wrong or something unexpected suddenly happened. Whatever it is, you should make it affect the characters. Give the protagonist a reason to do what they're doing.
After that it's pretty much just figuring things out. You can have the player progress through the incident and perhaps make small changes to it or its outcome, or perhaps find out more of a greater plot. Whatever it is, try to balance it with the gameplay. Don't go too long without any story, but don't throw lots of reading or confusing action in the player's face either.
There's probably a lot more to mention, but I don't really know if I'm the greatest storywriter myself, so maybe someone else has anything to add.
To make a story memorable, you need a good ending. To make the player interested, you need a good introduction. Take extra care with these parts. First impressions are often critical.