Save own fields in database
When you alter a node editing form, the fields you add are part of the node and can be accessed using the $node argument of hook_nodeapi. Save your data when $op == 'insert' and $op == 'update'.

If you do not want your fields to become part of the node, write a form submit handler and add its name to the $form['#submit'] array. The submit handler should remove all your fields from $form_state['values'] (in addition to whatever was intended when adding the field to the form).