Just copy the files from the old computer to the new one,
using a memory stick, network or any other convenient mechanism.
Then you can open the files with ADE on the new computer.
The new computer must be authenticated with the same account/ID as the old one.
If possible, copy the .epub/.pdf files.
They will probably be in your user 'Documents/My Digital Editions' directory on the old computer.
You can then open them on the new computer by drag-drop from Explorer or by Open (ctrl-O) in ADE.
If you only have the .acsm files you can only open them by drag-drop or double-click in Explorer.
The new computer will have to re-download the real .epub/.pdf files.
The .acsm files will most likely be in your Downloads directory on the old computer.