If you move the database you don't have to worry about licenses. As for the "how easy" it depends. Sometimes is just as easy as restoring the db to its new location, installing the app server and have it pointed to the new db location, some other times it requires a careful planning, especially if you have tools developed around service desk.
As I wrote migration can be as easy as restoring the DB to the new location, install the application server and have it point to the new db location and make sure that the db accounts on the application server correspond to a db account on the db server.
You have to make sure that the correct Service Desk SP is applied after installing the application server.
Having done the above, the server will be able to start. But functioning correctly greatly depends on other things as custom scripts you may have, dns etc...
In addition to George's post, in reference to HP OpenView there is Configuration, Customisation and integration.
Configuration lives in the Database - so the Business Rules etc you refer to will migrate OK.
Customisation is when Java stuff is modified or SQL triggers etc created. Many installations don't have these but you should try asking/looking for these.
Integration might be in the form of scheduled tasks initiating Data Exchange. This might be scheduled on the App server but could be elsewhere.
Finally it is easy to do a dry run and repeat it but you need to be a bit careful with the dry run that you disable the outgoing emails - or clients will get emails from the Production system and the Live system. So do as per the first post and immediately break the outgoing email settings (System Console, Email - first Tab).
Also if you have more than one app server joined you have to ensure that the test server doesn't try to join the live group - I am hazy on this so post for help.
It is then easy to connect one client to the test and see if all is working OK.