I figured it out. For example, in my Application_Model_DbTable_ExTable add
protected $_name = 'ExTable';
This way Zend will know which table in the database to use.
I then extended Application_Model_DbTable_ExTable to my Application_Model_ExTable, and once I did that I was able to insert into my database using an array such as
public function ExFunction ($example){
$data = array(
'example_column_name' => $example,
);
$this->insert($data);
}