If your website has a database, you will probably need access to your live database at some stage. In fact, you'll need to set it up in the first place!
Most (if not all) hosting providers provide access to your database. Coming to think of it, if your hosting provider doesn't provide you with access to your database, find a new hosting provider!
Many hosting providers allow you to connect directly to their database server using your own database management tools (such as Enterprise Manager for SQL Server). Others don't allow direct connections (for extra security) and therefore require that you use their online tools to manage your database. For example, your host might require that you log in to the control panel and use a tool such as myLittleAdmin, which is a tool built specifically for administering SQL Server databases remotely via HTTP.
Initial Database Setup
Whichever method you're able to use, you will probably need to run scripts in order to create your database for the very first time. You will also need to run scripts to enter its data. In most cases, you can generate these scripts automatically from with your database management tool.
Depending on your hosting provider/plan, you may be able to get them to create a placeholder database for you. You can then upload a .bak file via their job ticket area, or via FTP, and get them to restore the .bak file against the placeholder database. As mentioned, this probably all depends on your relationship with your hosting provider (and how much you're paying them!)
Once your database has been set up, you should be able to do things like run queries etc. You probably won't have administrator access (unless you've got your own dedicated database server), so there may be some tasks you need to get your hosting provider to do.
Depending on your SLA, you might not be able to perform backups. In this case, the hosting provider will be responsible for this. You should ensure that you are able to download backup files as regularly as you like. This might be in the form of requesting a backup from your hosting provider, or they might provide you with FTP access to a copy of the most recent backup files.
If backups are your responsibility, you should take this task seriously and perform backups regularly. Imagine if one day, the database server's hard drive craps out and you lose a year's worth of data?
If you don't have any backups, you're stuffed. If you do have a backup, you can quickly get your database back to the state it was in on the last backup.