Three steps: copy the files, copy the database, update the URLs.
- Files - zip
public_htmlon the old host, upload the zip intopublic_htmlhere, then extract. - Database - export it from the old host's phpMyAdmin, create a database and user here, then import it.
- Configure - edit
wp-config.phpwith the new database name, user and password. UpdateWP_HOMEandWP_SITEURLif the domain changed.
Alternative: install the All-in-One WP Migration or Duplicator plugin on both sites and import the archive. Send us a ticket if you would rather we moved it - migrations are free.