You can do that in a few different ways...
1. You can backup database on ad server, copy backup files to new server and restore on new one, just make sure you created the same users on new server..
2. Disconnect database from one server, copy database files to new server and reattach on new server,
3. Script database on old server, run script on new server to create database, copy data from old server to new server (but it may be problematic if you use identity fields and table relationship by identity values)