I've done this a large number of times. There is no "easy way" of doing it with replication in place. Basically the process is:

- Prep the new server for replication (setup the distributor)

- Get all apps using the subscriber databases offline

- Validate all subscriptions

- Resolve any validation errors

- Drop all subscriptions

- Drop the publication and disable replication on the publisher

- Backup the publisher DB

- Restore the publisher DB on the new server

- Make any changes you need on your database for and metadata relating to the old server to the new server

- Setup the publication on the new server

- Setup the subscriptions again WITHOUT INITIALISATION