I try to break my thinking down into two areas: a representation of the things I'm trying to manipulate, and what I intend to do with them.
When I'm trying to model the stuff I'm trying to manipulate, I come up with a series of discrete item definitions- an ecommerce site will have a SKU, a product, a customer, and so forth. I'll also have some non-material things that I'm working with- an order, or a category. Once I have all of the "nouns" in the system, I'll make a domain model that shows how these objects are related to each other- an order has a customer and multiple SKUs, many skus are grouped into a product, and so on.
These domain models can be represented as UML domain models, class diagrams, and SQL ERD's.
Once I have the nouns of the system figured out, I move on to the verbs- for instance, the operations that each of these items go through to commit an order. These usually map pretty well to use cases from my functional requirements- the easiest way to express these that I've found is UML sequence, activity, or collaboration diagrams or swimlane diagrams.
It's important to think of this as an iterative process; I'll do a little corner of the domain, and then work on the actions, and then go back. Ideally I'll have time to write code to try stuff out as I'm going along- you never want the design to get too far ahead of the application. This process is usually terrible if you think that you are building the complete and final architecture for everything; really, all you're trying to do is establish the basic foundations that the team will be sharing in common as they move through development. You're mostly creating a shared vocabulary for team members to use as they describe the system, not laying down the law for how it's gotta be done.