This thread might not be the most organized but all of the necessary info should be here. What have you tried? Here is an overview of the steps needed:
1) add the select list to your checkout page
2) update the code to make use of your new select list rather than the default shipping choice
3) if you need to display the option that the user selected use the switch statement and then use the session variable anywhere that you need to show this value
Please post back with any questions that you have about this.