Yes, I can tell you how they work. This is a subject I know very well. Stats is my business.
There are two types of systems. The first type examines the server logs, which keep track of all activity on the server. The service provider extracts data about the site visitors and presents it to the client - you.
The second type places a small bit of html code on each page you want to track. This is the most effective, as it gives greater, and faster, results. You also don't need access to the server. The html code extracts information about your visitors and sends it to the service. It is then compiled and results displayed.
The problem with most services is that they don't track ad campaigns or do sales tracking. Those that do charge a small fortune for it. Except for one that I could name.
Ad tracking monitors results from your individual ads. Sales tracking tracks the visitor from the source of the visit (Search, referral or typed in link) through the site to the final purchase.
Google and Overture will provide you with stats about the ad campaigns you are running with them, but many of your sales will come from other, maybe free, sources. Neither of these companies can provide data on sales from these sources.
The most important things you want to look for are the ability to compare performance over time, and present percentages of change. This will allow you to see how your site and promotions are progressing.
All good services will provide charts, but they sometimes can be hard to find a trend due to the violent swings in traffic and buying patterns. So a trend indicator is also a great help.
Let me know if I can offer any more detail. This is a complex subject that most people underestimate. Almost all web hosts provide some basic stats with your site. These are very rudimentary and will not provide the type of tracking you are asking about. They are ok for informational or educational sites, but for ecommerce sites you need hard marketing data, which is tough to get.
Regards,
Will
