I remember a similar experience when I had built my first MySQL website. I was used to building with the likes of MS Access and having a physical file that I could drag from one side of DW's ftp panel to the other. When it came to MySQL, I was damned if I could find the file to drag on to the ftp server.
Basically, there are two ways that I know of in which you get your MySQL db uploaded. The first is through phpMyAdmin which is hosted on your hosts servers. You log in there and simply paste the dumped MySQL code in to the SQL pane and click go... database uploaded. The second is use use something like HiediSQL which is a free GUI (google it). You log on to the remote server through the HiediSQL application on your local PC and paste your sql... remotely.
With HiediSQL, I build all of my databases locally, enter content into the tables and then build my sites. It's dead easy to build a site this way as you can see exactly what you're doing and you have content to test with. Once built, I export the database as sql, open it in wordpad, copy the dumped sql, use HiediSQL to log on to the remote server and simply paste the sql and click go (well, actually, it's a triangle, but you get my point).
It took me days to figure out how to get a MySQL database from my local PC to the remote server. Even if I have to upload with phpMyAdmin, I still use Hiedi to create the dump of the SQL in the first place. Hopefully I've helped, but if not, don't read this!