Alright, after some experimentation, I've discovered that it's pretty much the same thing up until the part where you are converting the selection to a path. You go to the Paths tab like in this tutorial, and then.....
1. Look for the button that says Selection to Path (in roughly the same area as shown in this tutorial), and hold SHIFT while clicking that button.
2. This opens a window with a bajillion slider bars. The value you want to edit is named Error Threshold; set it to 2-4 pixels like in this tutorial. Click OK.
3. Now you have a path named Selection. Unfortunately, GIMP will not let you fill a path directly, so you have to turn this path back into a selection. Still in the Paths tab, click the button called Path to Selection.
4. Choose the bucket fill tool. Under Tool Options for the bucket fill, you may want to have Fill whole selection checked, just to make lining several disconnected objects easier. (Tool Options is most likely docked under the Toolbox; if not, go to Windows -> Dockable Dialogs -> Tool Options)
5. Fill the selection with black.
6. Turn off your selections/paths/whatever and tada!
(written out for the benefit of anybody else reading the comments)
I can understand why, my poor litte bro has trouble with messy lines (he's just starting to learn), if he had something to smooth out his lines it would be a life saver for him. I should show him this 8D