Right from the Codex.

http://codex.wordpress.org/Child_Themes

 

Removing features.

http://code.tutsplus.com/articles/how-to-modify-the-parent-theme-behavior-within-the-child-theme–wp-31006

 

Pluggable functions and function priority. Removing Functions From Hooks.

http://code.tutsplus.com/tutorials/a-guide-to-overriding-parent-theme-functions-in-your-child-theme–cms-22623

 

Replace a non pluggable function in a WordPress parent theme with a customized function in the child theme

Replace a non pluggable function in a WordPress parent theme with a customized function in the child theme