Hey there tearie,
advice is right on or right arm whichever you prefer.
Once you've done the "drag and drop" of program icon to trash you might want to check in the User Library for remnants of the trashed program, sometimes in "Application Support" folder and drag that to trash.
OS X 10.4 has a feature in Finder drop down to securely delete trash, that is, overwrite over the file with code to make the file unaccessable. Use this with caution.