Install
TinkerTool and/or
OnyX on the machine you want to copy to. Either utility will allow you to make all files visible in the Finder, including invisible files, which you will need in order to copy all the user's files.
Next, create a user on the target Mac with the same name/pass as the user you plan to migrate. You have probably already done this.
Log in as that user, then mount the old computer in FireWire Target Disk Mode. Get Info on that volume and set it to ignore permissions on that volume.
Copy the contents of each subfolder in the old home folder into your new home subfolders. Some of the old files will replace existing files. By copying the files in as that user, all the files will arrive owned by the new user. This may take a little time if the user has a ton of stuff across many folders.
Afterwards, boot from the OS X Install CD and do a repair permissions on the volume, in case some of the replaced files needed special settings (like the user's keychain).
There are no doubt simpler ways to do this.