The simplest e-commerce solutions usually set shipping charges by dollar amount. Other solutions offer more robust models such as calculating shipping charges based on weight, or based on how many items can be packed into a box. Additionally, they let the customer choose which carrier they want to use and adjust the shipping charge accordingly. For example, the customer would be able to choose from Fed Express Overnight ,UPS Ground, UPS 3 Day, and Parcel Post for delivery. Simple e-commerce solutions let you charge taxes for your home state.
More complex ones handle international tariffs and taxes, non-profit sales and other situations.
Many e-commerce solutions, storefronts and shopping carts, take the order and simply send an email to you and the customer. Another option is to have order tracking. When the customer orders, the information is put into a database. You can then examine your orders from the web, or run reports off the database. You have a historical record of the orders which can be used to fine tune your product and sales strategy.