Right now, there is no real way to do that. You could log into Firefox Sync [https://support.mozilla.org/en-US/kb/what-firefox-sync https://support.mozilla.org/en-US/kb/what-firefox-sync], and that would move your personal data to the new computer (if it was using Firefox). but then you would want to delete your profile on the public computer to ensure you didn't leave your personal information available for others. There are initiatives that plan on making it possible to log onto Firefox from any computer and instantly have all your information, but they are not near completion.