How do you implement a class in C?

That depends on the exact “object-oriented” feature-set you want to have. If you need stuff like overloading and/or virtual methods, you probably need to include function pointers in structures:

typedef struct {
  float (*computeArea)(const ShapeClass *shape);
} ShapeClass;

float shape_computeArea(const ShapeClass *shape)
{
  return shape->computeArea(shape);
}

This would let you implement a class, by “inheriting” the base class, and implementing a suitable function:

typedef struct {
  ShapeClass shape;
  float width, height;
} RectangleClass;

static float rectangle_computeArea(const ShapeClass *shape)
{
  const RectangleClass *rect = (const RectangleClass *) shape;
  return rect->width * rect->height;
}

This of course requires you to also implement a constructor, that makes sure the function pointer is properly set up. Normally you’d dynamically allocate memory for the instance, but you can let the caller do that, too:

void rectangle_new(RectangleClass *rect)
{
  rect->width = rect->height = 0.f;
  rect->shape.computeArea = rectangle_computeArea;
}

If you want several different constructors, you will have to “decorate” the function names, you can’t have more than one rectangle_new() function:

void rectangle_new_with_lengths(RectangleClass *rect, float width, float height)
{
  rectangle_new(rect);
  rect->width = width;
  rect->height = height;
}

Here’s a basic example showing usage:

int main(void)
{
  RectangleClass r1;

  rectangle_new_with_lengths(&r1, 4.f, 5.f);
  printf("rectangle r1's area is %f units square\n", shape_computeArea(&r1));
  return 0;
}

I hope this gives you some ideas, at least. For a successful and rich object-oriented framework in C, look into glib’s GObject library.

Also note that there’s no explicit “class” being modelled above, each object has its own method pointers which is a bit more flexible than you’d typically find in C++. Also, it costs memory. You could get away from that by stuffing the method pointers in a class structure, and invent a way for each object instance to reference a class.