I'm not sure what kind of hosting panel that you have, but you should have a link to phpMyAdmin. that is the tool to manage your databases. If you don't see it check with your hosting company.
If you are using cPanel as your hosting control panel, then open the control panel and click on the icon MySQL When your arrive there scroll all the way to the bottom and you should see a link to phpMyAdmin. Once there you will have a list on the left hand side in the form of a drop down menu. Choose the database that is connected to your store.
Once there you will be presented with a screen that will give you an overview of your database. There is a button at the top "Export" click that and you will see a window listing all your tables on the upper left with an option below "select all" do that - When selected they should all now look dark blue.
Next on the right are some choices, The default choices should be just fine, except make sure you choose "Add Drop Table".
At the bottom right there is a check box to "save as file" check that, now click "go" (lower right) and you should be presented with a d/l box. D/L the SQL file and save it somewhere on your machine.
You've just backed up your database.
If you have any problems with this PM me and I'll email you some screen shots to help. I know the first time one starts mucky around with their database it can be scray.
Hope that helps.
Once you've got your db backed up, let me know (you can PM me) and I'll show you how to create a db.
Ruth