would be to create a home network, connect the two Mac's to it and turn on file sharing.
This assumes that you would also want to continue using the older Mac as a working machine with access to the internet.
If that is not the way you want to go, then just connect the two machines together with the Firewire800 to 400, start up the new one as normal and then fire up the old one while holding down the "T" key.
This puts the old one into Target Mode and you should see a bouncing Firewire icon on its screen. On the new one, an icon of the old ones hard drive will appear.
You now have access to that drive as if it were an external hard drive.
Are you the only person in the house that uses a computer?
My original 2009 Mac Mini runs OS 10.5.8 my new one Mountain Lion 10.8.2. I migrated files wirelessly with no problems but would now like the two Macs to be linked for backup purposes. What please is the best way of achieving this. For info old mac has Firewire 400 new one 800 can I use these, I have the correct cable...