Helpful resources (specifically to copy/move an existing site from an old domain name to a new one, which includes needing to copy/move the WP database, since the old site will still exist) for exporting and importing database onto new server:

  1. WordPress Codex
  2. Exporting and Importing WordPress
  3. WP Migrate DB (Migrate to a different domain and still maintain serialized data. Find and replace URLs and file paths.)