After connecting the two computers by FireWire cable you must boot one (the old one) into
Target Disk Mode. Then boot the other normally. The "old" computer's disk drive should appear on the "new" computer's Desktop. You may then us Migration Assistant to transfer from old to new.
Your new computer's user account that you created will need to have a different short name than the one you plan to import via MA as MA will not overwrite an existing account. If this is no longer feasible then consider moving your data manually.
Folders You Can Move to Your new Mac
From the Home folder copy the contents of Documents, Movies, Music, Pictures, and Sites.
In your /Home/Library/ folder:
/Home/Library/Application Support/AddressBook (copy the whole folder)
/Home/Library/Application Support/iCal (copy the whole folder)
Also in /Home/Library/Application Support (copy whatever else you need including folders for any third-party applications)
/Home/Library/Keychains (copy the whole folder)
/Home/Library/Mail (copy the whole folder)
/Home/Library/Preferences/ (copy the whole folder)
/Home /Library/iTunes (copy the whole folder)
/Home /Library/Safari (copy the whole folder)
/Home /Library/Calendars (copy the whole folder)
If you want cookies:
/Home/Library/Cookies/Cookies.plist
/Home/Library/Application Support/WebFoundation/HTTPCookies.plist
For Entourage users:
Entourage is in /Home/Documents/Microsoft User Data
Also in /Home/Library/Preferences/Microsoft
For FireFox:
/Home/Library/Applications Support/FireFox
/Home/Library/Preferences/org.mozilla.firefox.plist
Credit goes Macjack for this information.