Here we have another dense, religion-focused peice. To be honest I'm having difficulty wrapping my head around it.
When you have recourse to divination, remember that you do not know how it will turn out, but that you are come to inquire from the diviner. But of what kind it is, you know when you come, if indeed you are a philosopher. For if it is any of the things which are not in our power, it is absolutely necessary that it must be neither good nor bad. Do not then bring to the diviner desire or aversion: if you do, you will approach him with fear.
If you're going to seek the advice of the gods (presumably through a mortal proxy), keep in mind that you don't know what you will be told. But your philosophy does let you ask for advice without fear, if you keep in mind that things external to yourself are out of your control.
But having determined in your mind that everything which shall turn out (result) is indifferent, and does not concern you, and whatever it may be, for it will be in your power to use it well, and no man will hinder this, come then with confidence to the gods as your advisers.
This is great line, and in many ways a summary of a lot of The Enchiridion to date. Through Stoic practice, you learn to be indifferent to the things that happen to you, which allows you to turn them to your use. As a result you can approach life (or in this case, the gods) with confidence.
And then, when any advice shall have been given, remember whom you have taken as advisers, and whom you will have neglected, if you do not obey them. And go to divination, as Socrates said that you ought, about those matters in which all the inquiry has reference to the result, and in which means are not given either by reason nor by any other art for knowing the thing which is the subject of the inquiry.
This is where I start to get lost. This first part is OK - when you ask the gods for advice, maybe it'd be a good idea to listen. The next part seems to be saying: only ask for information about the outcome of a thing, not the thing itself. I'm not really sure what that means. Maybe the next section will help...
Wherefore, when we ought to share a friend's danger or that of our country, you must not consult the diviner whether you ought to share it. For even if the diviner shall tell you that the signs of the victims are unlucky, it is plain that this is a token of death or mutilation of part of the body or of exile. But reason prevails that even with these risks we should share the dangers of our friend and of our country. Therefore attend to the greater diviner, the Pythian god, who ejected from the temple him who did not assist his friend when he was being murdered.
OK, perhaps this is somewhat clearer. Don't consult the gods about what your actions should be; you should already know what the righteous thing is to do. You may consult them about the outcome, but that knowledge should not affect your decision.
Stepping back from the religious aspect here, I think the there are some useful ideas to take away. If you replace "consulting with diviners" with "contemplating the future", the advice becomes more practical. Thinking through the possible outcomes of a course of action is perfectly reasonable, but the possible outcomes should not prevent you from doing what is right.