Well I've never tried any of these programs so I can't tell you which one is better but check out these Keylogger Detectors. Some are built into anti-virus programs and others are standalone apps.

If you don't have access to install any of these on the PC then I'm not sure what your other options are.

http://download.cnet.com/1770-20_4-0.html?query=Keylogger+Detector&searchtype=downloads

Use a flash drive with spybot search and destroy and run it from the flash.

Easy. Don't use keyboard.

Well, it can be hard. First off, if it's a "public" system many times the admin of those systems don't want any 'software' installed on them and don't want to take the time to do it. If 'you've' experienced a 'security leak' and you suspect it's from that 'public system' you should report it to the 'attendant' and the admin. Sometimes 'they' will try to fix it asap... Sometimes not.

You might be able to uses SBSD on a usb drive, but you probably can't. I know it maybe hard, if you don't have your own system and don't have any other choice but to use a 'public' shared system...

No 'one software' is a 'complete fix' for such stuff, especially now-a-days where the loggers and other malware are so... "Bad", etc.

Hmm....