Export your WordPress database into a file. Import that file into another database on the new server. FTP your entire WordPress install, including theme, plugin, and media upload content onto your computer. FTP those saved files up onto the new server. Edit your wp-config.php file for the new database login credintials. If you are changing domains also: Edit via phpMyAdmin the WordPress options table. There are two entries for "url" and "wpurl" that hold domain values. Change those to match. Also run a SQL command to replace every occurrence of the old domain with the new domain in the post table. This will fix any links and image references in your posts. I don't know the exact SQL command that does this, but it can probably be Googled, or somebody may post it here. That is basically how to do it.
Well actually it depends if the domain will still be the same. Will it be on another directory or sub domain. But you can view the link below for a complete tutorial on how to move wordpress. http://codex.wordpress.org/Moving_WordPress