Hi Rebecca --
Yes, dragging the app to be disposed of to the trash and emptying the trash deletes the app. from your system.
But some apps come with their own uninstaller. When they do, the preferred method of deleting them is to use the uninstaller.
If you're wondering whether you've gotten all the files related to a particular app off of your machine, you can always run a spotlight search and see if anything remains, but in most (almost all cases) these straggler files (should they be there at all) are typically quite small and nothing to worry about.
-- JDee
PS Your stats note that you're presently running OS X 10.4.3. If that's so, you might want to think about updating to the most current version (10.4.5), as Apple recommends it for all users. You can update just by running Software Update (clicking the Apple Menu > Software Update) or you can use the
10.4.5 Combo Updater. In my view (and in many others') the Combo Updater is the way to go.