The short answer to your question is to go in your menu, open "Install / Remove applications" and find your software there, it will download and install all the software available in Fedora Core and Extras, including the mozilla suite.
There is a longer answer, it tends to get very long though. I'll try to keep it short.
1. Fedora is Linux. Linux is not windows. This is very important. Forget what you know about windows file management, as it doesn't apply.
2. Fedora is Linux, but Linux is not Fedora. Fedora uses the rpm system to maintain the software installed. This is one way to do things, and other distributions use other methods. You can even use other methods in Fedora if you'd like, but I wouldn't recommend it. You've chosen Fedora, stick with the Fedora methods.
3. Root is king. The root term defines both the root user which is the system administrator and the root of the file system, known as /. Only the root user can access all of the file system. For security reasons all software should run as user, not root. Users are limited to their home directory, and as such user actions can not bring down the system as a whole. Root should only be used for administrative, system-wide changes, such as installing additional software.
4. Files are spread around according to their function. If a file is a library, it will go to a library folder, documentation to the documentation file and binary, runable files to folders called "bin". This is very different from the windows approach which puts most files in a folder according to the application.
5. RPM keeps track of which files are located where, and to which appication they belong. If you install the mozilla suite RPM package, an entry for each file in that package will be entered into the database of RPM to keep track of it. So even though files are spread around the system, you can easily use RPM to track the files, and remove mozilla suite cleanly.
6. Rpm packages have dependencies. If software Y uses software X, package Y depends in X being installed to work. RPM solves this by refusing to install package Y without package X being present in the RPM database. This way rpm helps ensure that all the software installed will actually work. Because of this feature of rpm, manually keeping track of the dependencies of packages is a pain and known as dependency hell.
7. Yum uses rpm. Yum is a tool that downloads, checks and installs packages using rpm. It basicly automates the process of finding the right rpm package, it's dependencies, downloading them all, checking that the files are what they appear to be and installing/upgrading them. It's important to remember that Yum uses rpm, yum does not replace it. Yum, and other tools like it, is simply built on top of rpm to make things easier for the user.
8. Yum uses repositories. Repositories are web servers filled with packages and information about the packages. Yum has to get the packages and information about them from somewhere, that's the repositories. When you launch yum, yum will check it's configuration for enabled repositories and look in these repositories for information about the contents of the repositories. By default only the Core, Extras and Updates repository is enabled. Core is the content of the Fedora Core DVD as of release date. Updates is updates to Core. Extras is packages not included in Core. You can add other repositories like the Livna repository to get the stuff that can't be included in Fedora Core or Extras for legal reasons (like mp3 support). See http://rpm.livna.org/
9. It's not that scary and you don't have to care. Like I've said before, you don't have to know any of this. Just use the default configuration, use the graphical tool found in your menu, be happy.
Hope this helps somewhat.