The default database is in the Aeroware folder (C:\Program Files (x86)\Aeroware\Kitlog Pro v2.0\) and the default name is Kitlog.mdb. You can just copy that file over to the same location on your new computer. When you open Kitlog after moving the file(s), it will automatically show you your log if you kept the default file location and name. If you renamed your file, moved it, and/or have backup copies, you will have to search for them and copy them to the new computer as well. Once you have done that, open Kitlog and select Open Database from the file menu. This will allow you to select which database file you want to use.
The database (.mdb) file is the only thing Kitlog needs, so you don't have to hunt down settings files or anything like that. It's really easy to move and I keep a copy of my database on the computer in my hangar as well as a couple of locations at home.