Install LinkCAD on the other (target) computer. You should install roughly the same version as on your current computer. (Note: use the form at this location to download the latest version included in your license)
Start LinkCAD on the target computer, select "About LinkCAD..." from the Help menu. Write down the Serial Number.
Start LinkCAD on your current computer, and copy the above Serial Number to the "Transfer License" field in the "About LinkCAD..." dialog. Click on "Transfer" and use the displayed registration code to register LinkCAD on your target computer.
If LinkCAD tells you that the serial number is not valid, you will have to first install the same version of LinkCAD on your current computer. Just execute the same LinkCAD Setup on both computers, and repeat the above procedure.