How to delete cache after updating/deleting/adding new content using hooks? We have a custom services module and a site in Drupal 7, and I got the task to delete the cache after the editor adds new content or update the existing ones. 

I've read about a module called Cache Actions, but, as i said, i need to create the function on my custom module. 

Also, I've started reading about Drupal hooks, but still don't have a clue of how to implement this task. Any suggestions? Thanks.
It sounds like you've already got a custom module, but just in case you haven't see the Module Developer's Guide.

The hooks you're looking for are hook_node_insert() and hook_node_update(), and the function to clear the cache will either be cache_clear_all() or drupal_flush_all_caches. The former will let you clear specific cache bins (and even specific cache items), and the latter will clear absolutely everything. 

For example:

function MYMODULE_node_insert($node) {
  drupal_flush_all_caches();
}


or to clear only the static page cache after a node has been updated:

function MYMODULE_node_update($node) {
  $nodeurl = url('node/'. $node-&gt;nid, array('absolute' =&gt; TRUE));
  cache_clear_all($nodeurl, 'cache_page');
}