Rule of Thumb:
Old World wines come from the "classic wine making regions" aka Europe. New World wines come from "not Europe" aka anywhere else in the world wine is made.
Break It Down:
France, Germany, Austria, Italy, and Spain
Latin America, Australia, America, South Africa, and New Zealand
I love using maps when I'm studying wine. It helps me remember things. I also tend to write all over them. When I read about a wine growing region like the Mosel in Germany, I can write a bunch of things on the map next to "Mosel" like Old World, cool climate, riesling, and some top wine makers/producers (names I could recognize in the future on wine lists or at tastings). Or if I was working on a California map, for Paso Robles I'd note that it's considered part of the Central Coast and is recognized for its rhone blends and zinfandels.
Here is an example of a world wine map for this high level New/Old World exercise. When you start learning about specific regions, just work with regional maps!