I come from a movie/TV background, where often schedules and budgets are very small. I've found a lot can be done with paint--ESPECIALLY when it comes to zombies. A few dark and light colors are all you need for the basic look. You can even get by with some "Clown White" and some "Black", by just mixing some darker and lighter grays you can create all kinds of impressions of depth and shapes. You can bring the "shape" of a skull out by highlighting (the parts that stand out) and shadowing (the deep parts). Once the overall "big" forms are suggested, you can, if you like, sketch in finer details with smaller brushes, like wrinkles, folds, things like that. Then you can take a powder puff and some powder, and "set" the grease makeup (remove much of the oil, to make the color less prone to smearing). Excess powder can be removed gently with a clean powder puff, and the whole effect can be brightened by washing off some remnants of powder with a small white rubber sponge dipped in water.
Before I start on the real person, I will sometimes take a photo of the person (or someone similar) and sketch test versions of the idea over that person's photo. This can be done either physically with a pen and pencil, or using computer (virtual) tools, or mixing both techniques (as I have done above). I try to do this sort of sketch very quickly, as you see above, just to get the idea on paper and look at it, and I might do two or three versions and compare them and pick something that I like the most, and then try that out on the real person, using a printout of that image as a guide. You could call this a sort of "pre-visualizing" approach. It can often save time (and makeup materials) and help you develop a suitable look very efficiently.
A really, really good book that shows how to create stunning illusions with paint is Richard Corson's "STAGE MAKEUP". There are many editions of this book going back decades. Interestingly, many of the older editions focus more on older, more basic techniques like highlight and shadow. You can find this book in many libraries all over the place. When I was in school and learning the art of makeup (and learning never stops!), I would sometimes spend my lunch hour in the library reading this book. If you shop on Amazon, a used copy can often be found very inexpensively there, too.