There are a couple of ways you can do this.
1. Copy the user database from one computer to the other. (You can find the path to the database in Options > Global Preferences on the Paths tab). Then in Ultiboard, use Tools > Database > Merge Database to merge the data from the user database from the 1st computer into the other. This is the best way if you have a large number of footprints to merge.
2. Place the custom footprints in a design file (ewnet file). Then copy the file to your second computer. Open the file in Ultiboard, then use the Database Manger to import the footprints. Click Tools > Database > Database Manager. Select the target database. You will notice the "Add parts from the design to the database" button becomes active (it has a yellow plus sign with an arrow). Click Ok
Note: In this case, you do not want to use Tools > Database > Add Selection to Database. This will add the entire selection as a single reusable part, which is probably not what you want in this case.