Transferring files to new computer
You need to state what equipment you have (pc / laptop, home network / wireless and what you want to do. How much PC hardware manipulation skills you have would be nice as well as we cannot reccommend something you have no skill for.
For instance my answer could be to get several 5 1/4" floppys and copy the files across the systems. But since you posted under Windows 7 I have to assume this answer does not apply to your system(s).
The easiest method is to open up both systems and physically move the hard drive from the old system to the new system and hook it up. Instant file transfer.
If you do not want to keep the drive in the new system the next would be to copy the files from the old drive to the new. Then reinstall the drive to the old PC
This does NOT apply to software or the operating system as software needs to be installed and copying the OS to a new system is illegal and causes a whole raft of its own problems.
This assumes both systems are desktop models and not laptops, but you do not state. If laptops are involved then grab a network cable and hook the 2 together. Set up communication between the 2 units and start copying your data files across.
As for favorites lists and address books, they have to be exported and imported.