First of all you need the Backup and Migrate plugin installed and of course enabled this plugin is really usefull anyway!
Then you need to download the Backup and Migrate Installation Profile (above) and put the unpacked folder in "DrupalRoot / profiles".
Make a backup from your current Drupal-Page.
Upload the entire drupal folder to your new server.
Delete the settings.php in "sites/default" and make a new copy of the default one, rename the copy to settings.php
Start the installation like usual
Select the Backup and Migrate Profile.
Follow the steps.
Type in your new database infos BUT make sure to use the same database prefix as before, otherwise its not workin!
Upload your database dump
Now you´re ready to enjoy your Drupal :D