Try to identify the role of what you're rendering with any number of classes. This will replace the detail string. There is a predefined set of CSS classes which you can reuse where appropriate. Doing so will give you theming 'for free', whereas custom classes will require extra work in the theme. Note that complex widgets are likely to need different styles when rendering different parts, and style classes are one way to achieve this. This could result in code like the following (simplified) examples:

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static void
gtk_button_init (GtkButton *button)
{
  GtkStyleContext *context;

  ...

  context = gtk_widget_get_style_context (GTK_WIDGET (button));

  /* Set the "button" class */
  gtk_style_context_add_class (context, GTK_STYLE_CLASS_BUTTON);
}

Or

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static gboolean
gtk_spin_button_draw (GtkSpinButton *spin,
                      cairo_t       *cr)
{
  GtkStyleContext *context;

  ...

  context = gtk_widget_get_style_context (GTK_WIDGET (spin));

  gtk_style_context_save (context);
  gtk_style_context_add_class (context, GTK_STYLE_CLASS_ENTRY);

  /* Call to entry draw impl with "entry" class */
  parent_class->draw (spin, cr);

  gtk_style_context_restore (context);
  gtk_style_context_save (context);

  /* Render up/down buttons with the "button" class */
  gtk_style_context_add_class (context, GTK_STYLE_CLASS_BUTTON);
  draw_up_button (spin, cr);
  draw_down_button (spin, cr);

  gtk_style_context_restore (context);

  ...
}

Note that GtkStyleContext only provides fg/bg colors, so text/base is done through distinctive theming of the different classes. For example, an entry would usually be black on white while a button would usually be black on light grey.

Replace all gtk_paint_*() calls with corresponding gtk_render_*() calls.

The most distinctive changes are the use of GtkStateFlags to represent the widget state and the lack of GtkShadowType. Note that widget state is now passed implicitly via the context, so to render in a certain state, you have to temporarily set the state on the context, as in the following example:

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gtk_style_context_save (context);
gtk_style_context_set_state (context, GTK_STATE_FLAG_ACTIVE);
gtk_render_check (context, cr, x, y, width, height);
gtk_style_context_restore (context);

For gtk_render_check() and gtk_render_option(), the shadow_type parameter is replaced by the GTK_STATE_FLAG_ACTIVE and GTK_STATE_FLAG_INCONSISTENT state flags. For things such as pressed/unpressed button states, GTK_STATE_FLAG_ACTIVE is used, and the CSS may style normal/active states differently to render outset/inset borders, respectively.