For that you use a package manager application that knows how to do it; on RedHat/Fedora distribution that's yum (command line tool; there's also a graphical interface to it, but I can't remember it's name - check the menus..) You use it by telling it which package you want to install, then it checks (provided that it can access at least one reposity) if the available reposities have that package and if yes, download it and it's dependencies (if they are available - they should, that's the whole idea of a reposity) and install them. Try
yum install someprogram
or use the graphical tool.
"Automatic package managers" like yum or apt(-get) were created at least partly because of the annoying dependency trouble ("-hell" in the past), to get things done without spending days or weeks hunting for dependending packages. But note that the reposities usually only hold one version ("latest") of a package, and that's what the package manager gets (if it's newer than existing package on the system, or if it's not yet installed), so don't be upset if your package manager seems to install an "old" version of some package for you - the versions at the reposity are packaged and put there by people who might not bet paid for it, and definitely don't have time to create and upload new packages at the slightest change. Typically the reposities' packages are not the newest versions all the time - to get the very newest version of some software you probably have to compile it yourself (but is it worth it, taken into account the easiness of using a package manager + reposities with ready packages?).