This article explains how to download and install Firefox on a Mac.
When you first start up Firefox, you will be warned that you downloaded Firefox from the Internet. Because you download Firefox from the official site, you can click Open.
Also, Firefox will not be your default browser and you'll be told about that. That means that when you open a link in your mail application, an Internet shortcut, or HTML document, it will not open in Firefox. If you want Firefox to do those things, click Use Firefox as my default browser to set it as your default browser. If not or you are just trying out Firefox, click Not now.