You have a few options available. You can connect the two using Firewire and transferring via Target Disk Mode. If this isn't feasible, then you can connect each to your local network and transfer your files over the network. Be sure to enable File Sharing on each via the Sharing preferences panel.
If you cannot use Target Disk Mode, then you can transfer your data from the old computer to an external USB drive. When finished connect the drive to the new computer and restore the data to the appropriate, respective locations. This is more reliable and faster than using your network.
TDM will require you to purchase a Firewire adaptor for the new computer's Thunderbolt port.