First, if you haven't yet, enable Shipping for your products:
Go to Seller Admin>View/Edit/Delete Products;
Select an existing shippable product of yours and click Edit;
On the first screen, if Shipping/Buyer's Address is not checked there, tick that box;
Click Next until you can Submit changes;
Repeat this for all your tangible goods;
When adding new shippable products, remember to enable Shipping/Buyer's Address.
Go to Seller Admin > Cart Shipping Settings and set up the following:
Shipping Origin: select your country and enter your zipcode (if you're outside the US, just enter any 5-digit number);
Shipping Destinations: if you will only ship to certain countries, select them in the list, or otherwise select nothing for Worldwide shipping;
Leave all other settings blank or 0.00;
Click Next to save settings and proceed to the Shipping Rules screen.
In the Existing Shipping Rules menu, select and Delete anything you may have there.
Set up your first Shipping Rule for orders with only 1 item:
Shipping Rate Calculator: Flat;
Shipping Amount: (small flat-rate box amount);
Max Items in Cart: 1;
Click Submit to save the Rule.
Set up your next Shipping Rule for orders with 2-4 items:
Shipping Rate Calculator: Flat;
Shipping Amount: (medium flat-rate box amount);
Min Items in Cart: 2;
Max Items in Cart: 4;
Click Submit to save the Rule.
Set up your next Shipping Rule for orders with 5-6 items:
Shipping Rate Calculator: Flat;
Shipping Amount: (large flat-rate box amount);
Min Items in Cart: 5;
Max Items in Cart: 6;
Click Submit to save the Rule.
You will probably want to create at least one more Rule for orders of 7 items or more (just leave the Max Items in Cart setting blank/0 to have no maximum limit).
Click Back to Admin.