Building a checkout process in liveSite is as easy as creating a series of pages and linking them together. Each page has a purpose, which is set using the Page Types.
You need to plan out your pages from the Order Form page to the Order Reciept page. Then you create each page, assign the Page Type, and then link them together using the "Next Page" property of each page.
See the tutorial videos and online help manual for examples of the different types of checkout processes you can create.