In fact that’s not a one but four different questions :).
*) First you can quickly list a downloaded package’s dependencies/requirements by using the following commands:
$ rpm -qp mypackage.rpm --provides
$ rpm -qp mypackage.rpm --requires
*) Second, you can use yum utility in order to satisfy these (somewhat cryptic) dependencies automatically (assuming that all your repositories are set up correctly, and all the dependencies are available):
$ sudo yum install mypackage.rpm
*) Third, there are several RPM search resources, some of them already suggested above. I’d like to list another one, just for the reference – pkgs.org.
*) Fourth, there is an additional popular repository for RHEL5 and RHEL6 distros – EPEL. Note that it’s not supported by Red Hat.
Hope my answer(s) will help.