Probably the easiest way to do this is to add a new form to your cart page. The form only needs two fields, a text input for the zip and a submit button. Once you have this form in place you are ready to apply the shipping quote server behavior. When you do you will set the trigger to your new submit button being pressed.
This should trigger the shipping quote server behavior. Next you will want to check the shipping tab to see that you have your shipping quote charge there. If it is not you will need to add a new charge. You can give it a name then for the condition set it to 'shipping quote not empty' for your provider. For the charge choose based on shipping quote value for your provider.
The final part of all of this is to add a new cart display to the page. You wil need a new one to see the shipping charge. You can remove the existing one from design new and just add in a new one.
If you need any further info on any of these steps or if you encounter any problems let us know.
