old site - A
new site - B
Step 1 : download the wp_content folder (site A) to your computer using an FTP client (I like to use WinSCP)
Step 2: download the database (site A) to your computer. to access the database, go to the host control panel, then PHP my Admin, then click the wordpress database name, and then click "EXPORT".
Step 3: install a fresh WordPress on site B.
Step 4: upload the wp_content folder from site A, and transfer to site B (replace all the contents)
step 5: log in to the wordpress admin in site B, activate the new theme, and activate all the plugins you had originally
step 6: upload the database from site A over to site B. To do so, go to the new host control panel, click PhpMyAdmin, then click the wordpress database, then IMPORT
step 7: click this link:
http://interconnectit.com/products/search-and-replace-for-wordpress-databases/ and download the file "search and replace DB V2.1.0"
step 8: upload that file to your new host (in the public html folder). go to
www.mywebsite.com/searchandreplacedb21.php
step 9: search and replace any instance with your new website. for example, search for
www.siteA.com and make sure it is replaced by
www.siteB.com
step 10: once the tool is complete, test the website to make sure everything works good
step 11: delete the searchandreplacedb21 file once youre finished