I've avoided a thorough study of Illustrator's many functions up until now because it is, of course, an art program, and visual art was never my forte. In Grade 1, my art teacher had a special conference with my parents to address my inability to draw even the most basic forms, and even by high school concepts like perspective were beyond me.
I was relieved to discover that creating art in Illustrator is not like creating art in the real world. Drawing a perfect circle, for example, is trivial, whereas I doubt if I could do it on paper unaided. Since the first thing you learn is creating shapes without any fill, I started practicing by creating a variety of cell shapes that may come in handy. Creating, for example, a yeast cell with a mother and bud that is symmetrical is not quite as trivial as drawing a circle, but the steps involved are technical (don't require hand-eye coordination), and I quickly figured out a few tricks (e.g., if you want a symmetrical shape, you can worry about getting one side just right, then cut the shape in half and duplicate a reflected version of it). Modifying, recoloring, rotating, shading, even adding a "membrane" (border of a different color) is all trivial once you have the basic shape.
But the real gem of what I've learned so far is the ability to create new "brushes". In Illustrator jargon, a brush is a shape or set of shapes applied to a path (straight line). Particularly powerful are pattern brushes, which allow a user-created "pattern" to be repeated many times along a path, which can be straight, curved, contain corners, etc. If I can wax poetic for a moment, pattern brushes are a biologists dream: they work just like life does.