Building the UI: Really , really...easy
Right click on the DNNLINQSample module project and add a reference to the DNNLinqDBConn project.
Drag and drop a LinqDataSource onto the ViewDNNLinqSample.ascx file.
Configure the LinqDataSource as shown the steps below:
Step 1:
Choose the data context from the DNNLinqDBConn project as the datacontext

Step 2:
Choose the LinqSampleDB table
Click on Advanced and enable Edit, Delete and Insert operations.
Click Ok

Step 3:
Drage and drop a ListViewControl onto the ViewDNNLinqSample.ascx
Specify the DataSource to be LinqDataSource1
Then, click on the menu Configure ListView and Enable Editing, Inserting and Deleting

Note: Deleting the web.config from the module
If Visual Studio has added a web.config to your module project now might be a good time to delete it. It will give you an error of you try to run this module in DotNetNuke.
Step 4:
Log into your DNN installation as Host and navigate to Import Manifest
Choose the dnn file for your module and click "Import manifest"

Step 5:
Create a new page and select the module from the list of module to drop onto your page.

Your module should look like this:

Enter some data to test you module:

Thats it!
This is a very basic example to demonstrate the techinique that can be used to use LINQ and DotNetNuke together. My personal preference is to use LINQ only for the dataobjects that are pertinent to my module and continue using the DataProvider module for any DotNetNuke core data objects.
This way we wont break anything even if the core changes.