Most people adhere to the general rule: “between” is used for choices that involve two items, and “among” for three or more. You can also use the word “between” when you're talking about distinct individual items even if there are more than two of them. For example, "she chose between coffee, tea and water". Here, you can use “between” because the drinks are individual items. You can also use “between” in one-to-one relationships:
"she chose between the ball and the Frisbee", and
"let's keep this between you and me".
Those are examples where there is a one-to-one relationship -- you use the word “between” as opposed to “among”. Other times “between” can be used where there are more items when you’re referring to groups or people. For example:
"the negotiations between the lawyers, the buyers and the sellers were going well", and
"the differences between English, Chinese and Arabic are significant".
These are classic cases when you would use “between” even though it's more than two items.
Alternatively, you can use “among” when you're talking about things that are not distinct items or individuals. For example, if you were talking about colleges collectively you could say "she chose among the State schools". If you're talking about a group of people you also use “among”. For example:
"fear spread among the prisoners", and
"the scandal in the school caused uproar among the parents".
These are two very good examples of when you use “among”. Another instance where you use “among” is when you're part of a group:
"there is a code of honour among thieves", and
"upon returning from her long trip she found that she felt like a stranger among friends".
Here it indicates that someone is part of a group or they're left out of a group.
Another case is location. “Between” and “among” can also tell the reader different things about a location or a direction that they're taking. For example, when I give you these example sentences I want you to think about the differences:
"she walked between the trees", and
"she walked among the trees".
The first sentence, "she walked between the trees", gives you the idea that she stayed on a path or that she's either walking between two trees or she was on one route surrounded by trees on both sides. As opposed to "she walked among the trees". Here you get the sense, or you get the idea, that she was in a park or forest surrounded by trees all around. She's walking among trees. It doesn't sound as if there is a defined path.
That's a good way to see the difference between the two with respect to location and the feeling of the different contexts when you use “among” and “between” -- and the sense you get when you use both of them.
Finally, you can see it's not always as easy using the general rule that a lot of people follow, i.e. that between is for two things and among is for three or more things. Use the terms in the context and don't always follow the general rule.