I'm always confused by the problem "error: Failed dependencies"...
Could you someone introduce me a simple solution for that?

Very simple: use the package manager. If you're using Fedora: Applications > Add/Remove software. On Suse: System > Yast > Software management. On PCLinuxOS: Systems > Adminstration > Synaptic.

Failed dependencies means the package you want to install depends on other packages being installed first (usually libraries of some sort).

There are three ways to take care of the dependencies:
a) if the package is from the installation media for your distro, the dependencies are also there and will be installed for you.

b) manually chase down and install the missing packages.

3) install apt4rpm (versions available for RedHat, Mandriva, and SuSE; possibly others as well). Using the apt-get command and a sources.list that tells apt where to look for packages, apt will chase down the dependencies for you.

Apt has two GUI frontends: Synaptic and Aptitude.

If you really want to install program without dependencies you should use:
rpm -ivh --nodeps packet.rpm