Ideally... DON'T USE A PUBLIC COMPUTER! YOU DON'T KNOW WHERE THAT COMPUTER HAS BEEN (OR WHO TOUCHED IT)!
If you cannot avoid it... do a basic security check on said computer & check the following:
1) Check if there's any antivirus / antimalware software installed -- If you can't find anything like this running... GTFO that system & don't insert any storage medium in there! It's very likely the system is compromised & the staff managing that PC isn't paying attention.
2) Can you install programs freely on the system -- If you don't get any security prompts requesting an admin password, be wary of the system as it could be compromised by poor staff management & people who will freely install anything that's presented to them... like kids who want to play the latest free online game & don't care what "extras" are included in the installer (like toolbars, other bloatware & garbage that gets installed with the "default" options). Scrubbing the system is likely too much of a headache to deal with.
3) Check system specs -- Most likely, public computers have low-end specs... enough to run the OS & a few "light" programs, but not much else. It's uncommon to find any systems that would hit "Business Workstation" levels, much less gaming-ready specs, outside more professional areas.
Sadly, all you can do is make sure any unnecessary programs are closed & only run programs that you have stored on a USB storage device (ideally with applications from PortableApps.com so you don't leave any personal footprint or data on the system) OR possibly reboot the computer & launch your own OS (like Linux) from your own USB storage device, bypassing any software stored on the computer (& avoiding any questionable content that may be lurking on it).
You could mention the issues with the staff that manages the public PC... but you may not get far with them.