You need to look for the *.ost or *.pst file on your PC. You can copy that file to some form of portable media (USB stick, external hard drive etc) and then open it from Outlook on the new machine.
I'm using the aulder version, but same from what I remember:
File: Import & Export: Export
Choose a .PST file and make sure you include all subfolders.
Just the same procedure in reverse when you import to other Puter.
I find it easiest to click "File" > "Data File Management". You can then select each of your PST files (if you have more than one) and click "Open Folder", you can then copy these files to a USB stick.
If, like me, you have lots of accounts, and you can't be arsed to set them all up again, you could export the registry entries for it from REGEDIT... step by step instructions are here
You can backup the "autocomplete" "To" field too (you know, when you start typing someones email address or name on a new email, it brings up close matches etc so you dnt have to type the whole thing.) I can't remember how to do this though. I'll see if I can dig out the file. Then I might be able to tell you where it lived!!