These are the simplest: you want to provide a simple method which can act on your object. All you need to do is to provide a function prototype in the header and an implementation of that prototype in the source file.

/* declaration in the header. */
void maman_bar_do_action (MamanBar *self, /* parameters */);
/* implementation in the source file */
void maman_bar_do_action (MamanBar *self, /* parameters */)
{
  /* do stuff here. */
}

There is really nothing scary about this.

This is the preferred way to create polymorphic GObjects. All you need to do is to define the common method and its class function in the public header, implement the common method in the source file and re-implement the class function in each object which inherits from you.

/* declaration in maman-bar.h. */
struct _MamanBarClass {
  GObjectClass parent;

  /* stuff */
  void (*do_action) (MamanBar *self, /* parameters */);
};
void maman_bar_do_action (MamanBar *self, /* parameters */);
/* implementation in maman-bar.c */
void maman_bar_do_action (MamanBar *self, /* parameters */)
{
  MAMAN_BAR_GET_CLASS (self)->do_action (self, /* parameters */);
}

The code above simply redirects the do_action call to the relevant class function. Some users, concerned about performance, do not provide the maman_bar_do_action wrapper function and require users to dereference the class pointer themselves. This is not such a great idea in terms of encapsulation and makes it difficult to change the object's implementation afterwards, should this be needed.

Other users, also concerned by performance issues, declare the maman_bar_do_action function inline in the header file. This, however, makes it difficult to change the object's implementation later (although easier than requiring users to directly dereference the class function) and is often difficult to write in a portable way (the inline keyword is not part of the C standard).

In doubt, unless a user shows you hard numbers about the performance cost of the function call, just maman_bar_do_action in the source file.

Please, note that it is possible for you to provide a default implementation for this class method in the object's class_init function: initialize the klass->do_action field to a pointer to the actual implementation. You can also make this class method pure virtual by initializing the klass->do_action field to NULL:

static void 
maman_bar_real_do_action_two (MamanBar *self, /* parameters */)
{
  /* Default implementation for the virtual method. */
}

static void
maman_bar_class_init (BarClass *klass)
{
  /* pure virtual method: mandates implementation in children. */
  klass->do_action_one = NULL;
  /* merely virtual method. */
  klass->do_action_two = maman_bar_real_do_action_two;
}

void maman_bar_do_action_one (MamanBar *self, /* parameters */)
{
  MAMAN_BAR_GET_CLASS (self)->do_action_one (self, /* parameters */);
}
void maman_bar_do_action_two (MamanBar *self, /* parameters */)
{
  MAMAN_BAR_GET_CLASS (self)->do_action_two (self, /* parameters */);
}

These are very similar to Virtual Public methods. They just don't have a public function to call the function directly. The header file contains only a declaration of the class function:

/* declaration in maman-bar.h. */
struct _MamanBarClass {
  GObjectClass parent;

  /* stuff */
  void (*helper_do_specific_action) (MamanBar *self, /* parameters */);
};
void maman_bar_do_any_action (MamanBar *self, /* parameters */);

These class functions are often used to delegate part of the job to child classes:

/* this accessor function is static: it is not exported outside of this file. */
static void 
maman_bar_do_specific_action (MamanBar *self, /* parameters */)
{
  MAMAN_BAR_GET_CLASS (self)->do_specific_action (self, /* parameters */);
}

void maman_bar_do_any_action (MamanBar *self, /* parameters */)
{
  /* random code here */

  /* 
   * Try to execute the requested action. Maybe the requested action cannot be implemented
   * here. So, we delegate its implementation to the child class:
   */
  maman_bar_do_specific_action (self, /* parameters */);

  /* other random code here */
}

Again, it is possible to provide a default implementation for this private virtual class function:

static void
maman_bar_class_init (MamanBarClass *klass)
{
  /* pure virtual method: mandates implementation in children. */
  klass->do_specific_action_one = NULL;
  /* merely virtual method. */
  klass->do_specific_action_two = maman_bar_real_do_specific_action_two;
}

Children can then implement the subclass with code such as:

static void
maman_bar_subtype_class_init (MamanBarSubTypeClass *klass)
{
  MamanBarClass *bar_class = MAMAN_BAR_CLASS (klass);
  /* implement pure virtual class function. */
  bar_class->do_specific_action_one = maman_bar_subtype_do_specific_action_one;
}