As you now know from our two previous tutorials (namely "Facebook login at school" and "Facebook login at work"), you just need to have memorized your set of credentials (email address and password) to be able to login to Facebook from different computers. Since you can have several people using the same Facebook profile, the service will not prevent you from accessing your account from different places (even at the same time!) In this tutorial, we will give you a brief overview of the steps you should follow when you want to login to Facebook from someone else's computer.
The first aspect to keep in mind when you login to your Facebook account from someone else's computer is simply courtesy: if you are using the same user account (Windows profile, Mac user profile, etc.) as the person whose PC or Mac you happen to be using, they may well be signed in to their own Facebook account, and most probably have chosen to make Facebook remember their password - in other words, they are automatically signed in to Facebook unless someone logs them out.
If this is the case, and unless they have specifically allowed you to sign them out or clearly encouraged you to act as if you were on your own computer, you are faced with two options:

These 2-3 options are ideal when the persons whose computer you are using actually have a Facebook account; if they don't, you don't have the same concerns, but read on for other tips.
If the people whose computer you are using to login to Facebook don't have a Facebook profile, you will not have to worry about accidentally signing them out of their profile. But you then have to worry about the safety and privacy of your own Facebook account.
In that situation, all you have to do is manually logout of your Facebook account once you are done, and close the web browser window to make sure that no-one can (accidentally or voluntarily) end up inside your profile when they type "www.facebook.com" in the browser's address bar:
Between protecting access to your Facebook account, and avoiding to inconvenience other Facebook users' whose computer you may be using, you've covered all your bases!