I’ve observed elsewhere that sometimes people get into leadership roles simply because they were good at the technical aspects of their work, and so they have been promoted into a role in which they find themselves with people to lead. The Peter Principle applies here: people rise to their level of incompetence. Sadly, for many people, they reach their incompetence threshold the moment you ask them to lead other people.
In my time I have worked for several “leaders” who were in that category - highly competent in the technical aspects of the job but woefully incompetent when it came to leadership. I learned a great deal about leadership from observing these incompetent leaders and seeing (and being on the receiving end of) their inept behaviour.
What do you do if your boss is an incompetent leader?
The first thing you need to understand about that situation is that when it comes to leading your own people, you will be on your own. You will get no support from your boss, because your boss does not understand:
How to give you that support and
That such support may be needed in the first place.
Ask yourself whether you’re up for that, and whether it will even be possible to do your job under such circumstances.
If your boss is an incompetent leader, ask yourself a question. Is his/her behaviour at attempt to cover up a lack of self-confidence, or is he/she a psychopath? Either might manifest as micromanagement and/or an arrogant, "don't you dare question me" attitude. If you're faced with a boss who behaves like that and you figure that it's due to his/her lack of self-confidence then you might decide to step in and try to do something about it, but if you do that you're going to need a few very special attributes. All of these are important attributes in a leader, and this situation will give you an unparalelled opportunity to exercise and develop them.
Determination. Make no mistake, your life is not going to be easy if you accept this challenge, so you'd better go into it with your eyes open, determined to succeed.
Courage. You're going to have to be assertive and stand up for yourself and your people in the face of bullying and aggression, at least to begin with.
The patience of a saint. You can win this battle but it's probably going to take a while.
Humility, because if your ego ever shows itself it will get stomped on.
Empathy. The ability to imagine yourself in your boss's place, feeling as he/she feels.
Diplomacy. The Machiavellian kind. You will have to manipulate your boss in such a way that he/she doesn't realise what you're doing.
Your task, then, will be to "lead up," which is to say that you're going to have to step in and show your boss how to lead, but in such a way that his/her fragile ego does not feel attacked or impugned. It's a difficult thing to do, but if you spend time right at the beginning in building trust with your boss then it can be done. If he/she trusts you then he/she will be less inclined to see anything you do as an attempt to supplant him/her or make him/her look stupid.
So, building trust right from the start is vitally important. But then of course you know that, because it's true in every other situation you'll find yourself in as a leader. In this case, if you don't do it then nothing else you do will improve the situation and may well make it worse.
Once you've got your boss to trust you you'll be in a position to actively help out by showing him/her how you handle the role of a leader, and how your approach delivers good results. Look for opportunities to do that. Bring him/her into your workplace and invite him/her to observe one of your team meetings. Show him/her how you interact with your people, how you assign work to them and how you support them. If there's a leadership situation in which you know your boss is going to feel stressed and out of his/her depth, volunteer to assist.
What you are trying to do here is to show your boss how to lead, so that he/she can overcome whatever their difficulty is and start to develop some real leadership abilities of his/her own. If you can help your boss to become an effective leader, that's a win-win situation that will benefit not just your boss but everyone who works for him/her, including you, and of course the organisation as a whole.
I said earlier that if your boss is incompetent then you won't get any support from him/her. However, you are still going to need support from somewhere, and there are a couple of places you might get it. First, you might quietly "conspire" with your boss's boss, as long as that person is an effective leader who understands what you're trying to do and who will actively support you. If your boss finds out about this, there will be trouble, so be very careful! Next, look out for any colleagues you might have at your own level within the organisation, who are capable leaders themselves and who might be able to join you in your quest. Other ideas might occur to you, but whatever you do, don't underestimate the importance of having someone to support you.
A mentor, who's been where you are now and faced the same or similar challenges, will be of immense value to you as you navigate this difficult situation. A mentor will support and guide you and will help you to learn from the situation and from the challenges it throws at you.
A final point I want to make is that not everyone is suited to leadership, and not everyone is amenable to being led, however subtly, by a subordinate in the way I've been suggesting here. Some people who find themselves in leadership positions really are unwilling to be anything other than arrogant bullies, and in my experience this sort of person tends to surround him/herself with similar types. When a psychopath gets into the CEO's role, soon the entire senior management team will be made up of psychopaths, too, and when that happens you face a difficult choice: keep your head down and wait it out, because inevitably they will fail and will be ousted sooner or later; or quit while you're still sane.
Whatever you choose to do, pick your battles carefully and above all never compromise your personal values.