Well we have this Linux Server on campus that we have to turn projects in to; and so far I've been just like the rest of the Windows Idiots, and using a program called PUTTY. I want to be able to access the server directly from my Terminal window in Fedora. I have figured out some of the "SSH" stuff; however when I connect to it, I am immediately asked for a password and never requested to enter my login. I am authorized to access this server, for I have a login and password. I can't figure out how to get past this hurdle and my professor is not responding to his email. I think he's tired of this "Linux Newbie"...

man ssh will help there.You can ssh directly from terminal

What do I do when the first thing it does is ask for a password? The one I have, that's associated with my login on that server, doesn't take...

Is your username on your local box the same as it is on the ssh server? If not, then you might want to try specifying the remote username on the command line. For instance:
As far as I know, ssh defaults to the current username when it's invoked. In other words, if your username is klmbrt, it will default to logging into the remote machine as user klmbrt. Typically though, you have the chance to change it. Then again, things may be set up differently with their server.

If that doesn't work, then I'd review what settings they tell you to use in PuTTY, and see if you can match up those same values with the options ssh provides in its man page.