If you are using cPanel than there should be database backup tool from there you can export yoru existing site database than import to new one..
If not than
go to PHPMYADMIN > Your Database ( root )
Find Export tab at the top than click export
go to your new server and phpmyadmin > database root
than find Import tab and import thd database you exported in step 2
Than from qa_option table chnge yoru site url with new url
If you are using the same host provider than you don't have to do anythign but just change your site url in qa_option table and use same userid pass to new site..