To transfer your drupal website you must to back up database first. To do this start your apache server and web browser. Enter http://localhost in the address line and click on phpmyadmin link in the opened window. Click on existing drupal database. This will open your database window. Find export link and click on it. At the bottom of the window enable save as file and click on Go button. Choose directory where you want to save it.
Next step is to create a new database on your remote server. When this will be done click on import link and import just saved database on your computer.
After this will be done your must to transfer all drupal folder from your computer to your website. The best way to do this is via FTP. FileZilla will do a great job. This will take a while so you can have a cup of coffee or something else.
The last what probably you will need to do is to change your settings.php file in sites/default directory. Under database settings enter database name, database username and database password. You will must to do this only if any of these changes was done when you was creating database.
I will publish tomorrow step by step guide on my website how to transfer drupal website and you will be able to look on it if will have any problems. Or post comment here.