I never trust free proxies.
That said, I have, in the past, made the mistake of accessing encrypted (HTTPS) pages with private information while using free proxies, and I have never suffered for it. I avoid it at all costs, however.
As a general rule, I use the proxy ONLY when and where I need them, and disable them as soon as I don't need them.
As for using them, a proxy is nothing more than an IP address and a door number. In Firefox, you go into Options > Advanced > Network > Settings..., select "Manual proxy configuration", tick the "use this proxy server for all protocols" checkbox and put in the IP address (123.45.67.890, for example, it's a number like this) and the door number (8080 or something) and click OK.
Then you test the connection. Often times free proxies will not work as intended and you'll need to test another one.
Unfortunately, it's not a one click job and it may require patience. Such as the woes we must suffer through in the name of information....