There's a couple of ways you could accomplish this: One is to back up the database, layouts, etc from each tab. Since you're wanting to go to a different computer, you'll want to back it up to a flash drive.
Another option is to go to the C:\Users\<Your Log in Name>\Documents and copy (or move, won't matter since you're seemingly not going to use the old one) "The Tournament Director 2" folder to the flash drive. In either case, you'll want to paste it on the new computer to the same location. You'll have to download the program agaiin from the main site, but you can put in your information again.
On the new computer, you may need to redo your preferences - if you do the second route, you shouldn't need to, but may need to not as much.