If you don’t have an FTP client, I would suggest FileZilla. It’s opensource, easy to download and install, and works great. Click on the Download link in the FileZilla section of the menu.

Finish installing FileZilla and start the program. Pull up the Site Manager from the File menu. Fill in your URL in the Host field. Enter your Username and Password in their fields and click Connect.

Once you are connected, Filezilla will show a tree structure of your computers files on the left side and your hosting account files on the right. There’s another section below the tree structure to show the contents of the current directory.
Navigate the left side to your wordpress directory on your computer. Copy the contents of the wordpress directory and the sub-folders over to your hosting account.
Don’t make a wordpress folder on the host site unless you want to access your wordpress blog using this directory in the URL. Without this folder, you will access your wordpress blog directly from your URL: http://www.yourhostingsite.com.

If you have a WordPress directory on your host, your URL would just be: http://www.yourhostingsite.com/wordpress/.
Upload all of your files, but don’t try to access your site yet.