If you are using Fedora then you need to know root's password (which is different than your password) when you try to switch user with 'su'. Who wiped the system before you got it? Didn't he tell you what root's password is?
If you don't know root's password, you might be able to gain root privileges with the 'sudo' command (for sudo rights, the root user has to put you in the sudoers file). You can switch user to root by running the command 'sudo su', and when you are prompted for a password - give **your** password this time.
If sudo doesn't work for you, and you can't get root's password either, you may have no choice but to reinstall the system.
Once you gain root access, you can install software by either getting it from the distribution's repositories (this is the most recommended way), or getting the rpm package and installing it locally. To see if skype is available from the repos, run the command 'yum install skype' or 'yum search skype'. To install from the rpm you downloaded locally, run 'yum localinstall <rpm_file_name>'. The 'yum' command handles downloading all the needed dependencies and installing automatically for you.