How can I delete my own node comments?
There is no permission in a default D7 configuration to only delete one's own comment. To get this you must install Comment Access (or another contributed module with a similar function).

If you add the permission "Administer comments and comment settings" (navigate to Administration » People » Permissions), to a role, that role get access to a "Delete" tab for comments, but that lets the user holding this permission delete everbody's comments - not only his/her own.

Installing a module is no big deal in Drupal.  If you want this, I am afraid you need to install a module.