The most rudimentary Rails app consists of nothing much other than CRUD operations on tables in a database. Nothing special about what kind of database, you just have to say what kind it is in the config/database.yml file.
Basic scaffolding generates models that fit the exact scenario you're describing: create, read, update, delete (CRUD) records in various tables in your data base.
If you're database tables have relationships that you care about, you need to dig a little deeper of course, and look at ActiveRecord relationships.
Assuming your postgresql database already exists, you can still run the scaffolding generators for it, but it becomes a bit more complicated from then on. You don't want to run the migrations they generate, as they will destroy the existing database. Likewise, using rake to run tests will fail as it checks to see that all migrations have been applied.