General :: Installing And Running Downloaded Applications?

As a long time Windows user, I am stuck on the basics of installing and running downloaded Linux applications. I've tried to read a few tutorials but am still baffled. I am using a Puppy based boot CD and, of course, the applications that come with the Puppy all work fine. It is when I try to add something new that I become lost. Example: I just downloaded a Linux version of the Firefox browser.

I click on the downloaded file in the Download Manager and kinda expect the thing to give me a executable set-up file, but just get a whole bunch of files. One available option is to "extract" them. I create a folder to extract them to and "extract". With Firefox I see nothing in that folder. With a few other applications, I see an extracted list of files but and try to find one file that will magically start and install or boot an application, but nothing ever happens. So, how does one download , extract, install, and then run a basic application? The references I have found on the Internet tend to be rather old or more complex that my brain can handle.