Simple Question

How can I connect my two 10.5.5 computers in order to transfer files from one to the other?
The new is a Macbook Pro. The old is a G5. Both are running 10.5.5. I am up and using both fine -- connecting to the Internet, etc.
I realize that is the most basic question ever asked. I humbly accept this.
I've actually spent a whole lot of time trying to figure this out -- from Apple's site, forums, other sites, etc.
I'm trying to set up a network with my 2 macs. I couldn't make a connection occur between them, even though I did what Apple's site said. ie, turing on file sharing, screen sharing... Well, I should say I can see the other computer, vis-versa, but the only files I can get to are in the Public Drop Box. Is there a way I can get to the entire Mac?(ie the music and photo folders are my main concern) I've turned on Appletalk and even used the finder Go-> connect to server and put in the address. I even created a network under the Airport and joined the 2 Macs, but again to no avail on getting to the whole mac.
The folders are grayed out or have the little red stop signs in front of them so no access
Maybe the question is so basic that it's right in front of my face... I can think of no other reason on why I can't find a step by step guide to do this.
Thanks ahead of time for helping me out with this.