How can I know what username and password my proxy is using if I am not the administrator?

What do you mean what it's using? Your proxy is a server, it wouldn't use a username or password to be a server...??

http://http://fedoraproject.org/wiki/Docs/Drafts/SoftwareManagementGuide/YumProxy

If you go through the link theres a proxy username and password.What do I have to set in my case is what I am confused?

erm.. ok... the vagueness of the question suggests that you might not even be sure that there IS a proxy...

you get the username / password for a proxy by configuring it under your own designs, or asking the person / team responsible for configuring it. there's naturally no "default" there... maybe you don't need one at all?

.I am sure that I am using a proxy.All I want to know is is there a command or something where I can get the user name apart from asking the one you has configured it.Cause I cannot do it here.BTW configuring only the proxy setting has helped me restore the yum command now its working.Thanks for all your help.
Now I have one more question I have installed it on my guest OS(fedora).Now the next time I reboot the OS.I want all my settings to be as it is i.e. I need to have all the softwares installed and usable the next time I boot.How can I do it?

A command that will give you a password? does that sound likely?

Software doesn't uninstall itself while the system is turned off. Most things should be as you left them.