Using any computer that doesn't belong to you, is a huge potential security risk.
Computers in libraries and internet cafes, are all under the control of others, and therefore should be used with extreme caution.
As we always say, trust nobody, and expect that the public computer you're using will be full of keystroke loggers and software that logs everything you do.
DO NOT LOG INTO ONLINE BANKING ON A PUBLIC COMPUTER. THIS IS ABSOLUTELY ESSENTIAL.
We would even say, don't log into your email or webmail accounts when using a public computer, because you seriously run the risk of having your log in details stolen.
Anything you type into a public computer can and probably will be copied and stored.
Even if you think that your email details are not that critical, imagine somebody having direct access to your mailbox and everything in it, that has been sent or received. This will almost certainly include sensitive and private information, and will probably then allow access to other login credentials by way of what might have already been stored in your Mail, or might be when the person snooping decides to have your 'forgotten' password emailed to you/them.
That's why your email protection is extremely important.
The other aspect to public computing, is logging on to free wi-fi, in places like cafes or public areas.
Always assume that whoever controls the router, has a means of getting on to your system when you log on to their wi-fi.
There is also the possibility that another user on the same wi-fi network could gain access to your machine.
Firstly, make sure you un-check the option to connect to networks automatically. You need to approve this every time, so that you know exactly who you are connected to.
Secondly, make sure you OS firewall is switched on.
Thirdly, make sure that all file and printer sharing is turned off.
This gives you some protection against malicious attack.
For greater security on a public wi-fi, we would strongly recommend you connect through a VPN. This effectively wraps all your data coming out of your laptop, in a secure tunnel, direct to the source, meaning it's extremely hard for anybody to intercept your traffic.
If you've recently logged into webmail or email on a computer that is not your own, we recommend you change your email passwords. In fact, it's a good idea to change them regularly anyway.