you could also download portable apps from portableapps.com
they have firefox, chrome and a few other browsers along hundreds of other apps that will run off a flash drive without leaving a trace on the host computer.
Are you open to using ANY browser, whether it be Chrome, Firefox, Opera? Or do you have a preference?
You can force Firefox to launch in incognito, same with Chrome and possibly Opera. IE too, but not portable. And tell them to delete browsing history etc afterwards.
Alternatively, you can run the program under the supervision of Sandboxie Free and delete contents once all processes have ended. Applies to both portable and installed.