What is the difference between dependency and association?

In general, you use an association to represent something like a field in a class. The link is always there, in that you can always ask an order for its customer. It need not actually be a field, if you are modeling from a more interface perspective, it can just indicate the presence of a method that will return the order's customer.

To quote from the 3rd edition of UML Distilled (now just out) "a dependency exists between two elements if changes to the definition of one element (the supplier) may cause changes to the other (the client)". This is a very vague and general relationship, which is why the UML has a host of stereotypes for different forms of dependency. In code terms, such things as naming a parameter type and creating an object in a temporary variable imply a dependency.

You don't want to show every dependency on a UML diagram - there are far too many. You need to be very selective and show only those that are important to whatever it is you are communicating.

I tend not to use stereotypes on the dependencies very often. I find that most of the time the key point I want to show is that a dependency exists, and which kind is rather less vital.

Associations also imply dependency, if there is an association between two classes, there is also a dependency. But I can't imagine a case where you would show that dependency as an extra line on the diagram. The association implies it, as does a generalization.

One source of the confusion was the use of transient links in UML 1. These appeared due to meta-model problems in UML 1. They manifested themselves as stereotypes of association such as parameter. I've always disliked these since I think the difference between a permanent slot and a relationship that's only present within the context of a method is rather important. As a result I would use such stereotypes on a dependency rather than an association. In UML 2 this issue no longer arises, since the meta-model has a different way of handling method scoped relationships, so such stereotypes are no longer valid in UML 2.