The rpm command is on of them with endless options. However, you will probably use the -q "query", -e "remove", and -i or -U ( "install" and "Update") options, so remembering three sets of options will cover you 98% of the time.
rpm -qa | grep <part-of-package-name>
is a common command I use to see if a package is installed and lookup the different packages with similar names, such as "rpm -qa | grep xine" which will display packages with xine in them, which will include packages with plugins and libraries.
rpm -qi packagename will display information about a particular package. "rpm -ql packagename" will list the files on your system that the package installs. Another very handy option is to list which package installed a particular file on your system, for example:
rpm -qf /usr/lib/sgml-tools/linuxdoc-sgml.sty
You can also use your distro's packaging system to do all of this as well, however for packages that your distro doesn't supply, you may need to run the rpm command manually.