As far as I'm concerned, acceptance testing should be conducted by the people who you'd like to find the application acceptable -- without scripts or detailed instructions. I recognize this isn't always possible, but it is the only way to really know.
Lucky for you, it sounds like you have websites in production that you are regularly updating/enhancing. This gives you a *huge* advantage in that it is quite easy to find out what users actually do on your site. In fact, your IT or production support team probably already has weblogs that track (hopefully anonymously) user activities that you (or someone else) could parse to give you some insight into how your users are using the system.
If these things are not being logged, it's simply a matter of setting that on the Web server. You may even have tools in house that parse the log files already. Again, your IT or production support staff will know. I recommend asking them what usage information they can provide for you, and if that information isn't adequate, see what you can do about getting a monitoring tool in place. If you need a tool, once again, you're lucky. Many are free. One of the most popular is Google Analytics, all you'll need is for developers to add a short snippet of code to the bottom of each Web page, then you can access analytics from anyplace you have an Internet connection and browse site usage data in near real time.