I'm going to write a detailed post about reducing risk when using random computers whilst travelling - simple measures which you can take to protect you and your data. Until then one very quick, very simple and very important one.
Use the logout button.
If you are using a public computer to access the likes of e-mail and Facebook then make sure you use the logout button once you are done. I have seen it all too many times when people don't - I've sat at computers where I've found people signed-in to Chrome/Gmail/Facebook, giving me them access to a lot of stuff I suspect they don't want me or anyone else to have access to.
Use the logout button; wait until it is confirmed you are logged-out (e.g. back at the login page) and then close the browser (i.e. close all the browser windows for that browser). Congratulations, you are now less likely to have opened-up your life to exposure you probably don't want.
You should also consider the use of the "private browsing" mode in most (all?) modern browsers, as this helps prevent leaving your "trace" on the computer - just remember to close the browser after.