How would one convert used vegetable oil into fuel for home heating in a fuel oil heat system?

You want to turn it into biodiesel, but it's not a trivial thing to do, and - unfortunately, there are technical issues with burners, viscosity etc. that mean that it's not that easy to convert over to pure biodiesel in the heating system. At present, most companies who are selling biodiesel for home heating are selling it as a mix with conventional oil.

If you want to learn more, however, there are a lot of biodiesel sites out there - Google biodiesel, and you'll find all that you need to know.

One good site is journeytoforever: http://journeytoforever.org/biodiesel.html

My guess the same way that you do with bio diesel. You filter all the rubbish out. Boil off any water impurities. And treat it with methylated spirits and remove the glycerine.