Method One - Google search
You can find out what Google has indexed by returning results the exact results by searching for
site:http://www.example.com. You should be aware that this method may not track very new URLS or if you have a lot of pages then Google will just return a few hundred.
Method Two - sitemap
There might be a sitemap.xml already on the server and you should be able to use that but you should also be aware that if the sitemap is not updated it may be obsolete. You should do both sitemap.xml and
site:http://www.example.com just to confirm it is.
Method three - low volume of URLS (pen and paper)
Another favorable method is simply navigate through the website and of course write down the URLS. After your done you should proceed to ensure that you have them all by doing a good old
Method four - copying old site to a hidden sub domain
Often I will copy old site information to a secured sub domain that requires a password, this is a good way of having a backup and referring to the old site even after the project has been delivered. You can copy the site using FTP and backup the DB using phpmyadmin and then port over to a sub domain. Or alternatively you can convert the site into a static HTML site by using HTTrack.
Updating content is not a guarantee increase in rankings and cab be negative
It's important to note that when changing content on the majority of the website in question that you should inform your client to expect a shift either positive or negative, if the content is high quality, unique and not over optimized you should expect the negative to be temporary. Normally negatives result as too much optimization, over thinking URLS, Titles, and so on results in this way.