Pertains to a Windows machine..
Definitely get other opinions on this. I last did this myself in 2010.
The most important thing, is to make sure you have an account (which I think you must have, or you probably couldn't have posted here).
As I recall, I downloaded ADE to my new computer, launched the software, authorized the new computer by supplying my login, and then just moved the 'My Digital Editions' folder to the new machine.
Be sure to de-authorize your old machine after you have done all of this, or over time you could end up exceeding your 'simultaneous devices'-limit for accessing your materials. I suspect that *from within the app itself, while it is still installed on your old machine* may be your only opportunity to do this. It is certainly the best/easiest.
Hey Internet! Have you done this more recently than I? If so, please chime in to make corrections or add detail.
Were you able to retain the books that were on your original ADE