Do I have my external hard drive set up correctly?

I'm a relatively new Mac user. I have Mac OS X 10.5.3 and an Airport Extreme which I use as our home network. I have a Lacie external hard drive connected to the AEBS. As I say, I'm a newbie, so my total experience is Windows. In Windows this hard drive would show up as a new drive letter. On the Mac, by contrast, the drive does not always show up in Finder. I can make it show up (I think) by clicking Time Machine Backups and then the volume (which ends ".sparsebundle"). Apparently I can manually save files to the drive when it shows up this way. When I click the eject icon, the drive goes away.

Is this correct, or have I botched it? Please confirm or help, and if I've done it wrong, please be explicit in your suggestions as to what I should do, since this is new to me.

Thanks.

Stuart

Maybe try not ejecting the drive?