One thing most people wont do, either because they have no clue about it or have something to hide, is put
Google Analytics on the pages of the site. Using this, you can see exactly where the traffic is coming from, type in, search engines, what website is reffering the visits. You can also see what country most users are from, how long they stay on the site, and much more.
If they have google analytics installed in the site, they can just add your google email and give you access to view the reports. You can easily see if they have an influx of some paid traffic etc from these reports.
These reports are way more accurate than things like Webalizer and AW stats imo, because alot of the traffic that shows up there are web bots crawling your site.
Good luck!