Being new to Macs I have a tendency to download and try
out third party software and in turn remove the ones I
donīt like. On a Windows PC I would use the Add /
Remove programs function to do this. How do I most
efficiently remove an application on my Powerbook and at
the same time being sure that the program doesnīt leave
behind any residue? So far I simply drag the application
file to trash, but this seems to leave behind quite a bit of
files connected to the trashed application.

CEE

Most programs should be removed by Trashing them. You are correct that many will leave files behind (such as .plist preference files, cache files, or other support files, depending on the program.) Some other programs do include a Remove option, usually as part of the Installer.

For the most part, any files left behind after a program was Trashed are harmless; that is, they don't take up much disk space and they don't interfere with other applications or the OS. (Unlike Windows, Macs don't have a Registry, nor do they experience "dll hell.") If it makes you feel better, you can look around and delete them (again, drag them to the Trash) but it's almost never necessary. These support files mostly hang out in the system Library/Preferences, Library/
Application support, and the corresponding folders in your user account folder.