I'm a newbie and when messing around with creating database applications I always just created my forms and put all the code and bindings in there. Instead of having arrays and lists that held information I made changes to the database directly.
Now that I have evolved a little bit let's say that I sold widgets to customers and kept the sales information in a database. If I were writing a program to access the database wouldn't I want to create a class of type 'Customer' and 'Widget' to work with those entities?
If I'm mistaken then what is the appropriate approach to programming database applications?
Yes.
You want to look into n-tier programming.
Basically, you allow you front end (presentation layer) access only to your class library (business layer). Your class library then accesses you database.
This gives you a less tightly coupled solution, and allows for more maintainable code. Also by introducing tiers you allow for changes to your DB without the need to rewrite code in your frontend, as long as the interface with the Business Layer doesn't need to be changed.
As far as binding is concerned, if you are using Visual Studio Windows Forms (2005 onwards) you should be able to us an bindingSource that you can then use to bind your controls. If you are using ASP.NET then your control should bind to a list of objects without any problems.
For ASP.Net the ObjectDataSource might be worth looking into. I haven't used it myself, but there's lots of samples on the web. Try here or here.