In your language of choice:

    static_function(db, other, arguments) { ... }
    test { static_function(fake_db, 1, 2) }

You can even omit the db in the standard case if your language allows default keyword arguments. In almost every language, a method is just a fancy static call that takes extra arguments implicitly. (Closures are poor man's objects, objects are poor man's closures...)

So how exactly do you test that your SQL query does the right thing? That you're using the Twitter API correctly?

Testing a database, or an external web service, is an integration test. They can be as simple as:

    void TestCreateUser() {
        var repo = new UsersRepository();
        var mockUser = new User("John", "Smith");
        repo.AddUser(mockUser); // db call
        var addedUser = repo.GetUsers().Single(); // db call
        Assert.StructureIsEqual(mockUser, addedUser);
    }

For the Twitter web service, you might test that you successfully get a response, as you don't have control of what exactly comes back.