1. Install a new JobScheduler on the new server.
  2. Copy the ./config/live/ folder from the old JobScheduler to the new JobScheduler.

That's all!

Well, not quite. What happens with the database?

The new JobScheduler doesn't need the old database records.
The configuration of the jobs, job chains, orders, etc are stored in the ./config/live/ folder and not in the database.
But you cannot see, for example, the old logs.
See Which information is stored in a database by JobScheduler? for more information about what JobScheduler stores in its database.

To see the the old logs and other information stored in the database in JOC, you have to migrate the database.
The tables which are used can be found in ./db/[dbms]/scheduler.sql.
Note that all of these tables have the ID of the JobScheduler as a (part of their) primary key.
The records with the old JobScheduler ID will then have to be updated with the new ID.