I hate to say it, my friend, but learning to listen is largely about changing your attitude towards the people around you. It is very difficult to listen when you perceive that you're miles above everyone around you. Consequently, the first step is to learn to see how wonderful, competent and intelligent every single person around you is. If the people who surround you are (in actuality) neither competent, intelligent or even remotely wonderful, run (don't walk) away and find new people!!! :)
Once you have built a genuine interest in the people around you, good listening skills naturally develop. When you're interested in the people around you, you will hang on their words, ask probing questions and reflect back what you heard to make sure that you understood it.
If you can't engender a natural interest in the people you surround yourself with, you can fake an interest. To do so, I recommend getting in the habit of repeating back things that you hear, nodding in agreement when the person says something you agree with, not interrupting when they say something you disagree with, and asking probing questions when you don't understand/agree with something.
Have you ever considered Toastmasters? It sounds silly to join a public speaking group to become a better listener, but I can't tell you how much Toastmasters helped me!
Just keep your mouth closed. That's a first step. Resist the temptation to solve problems - as that is no longer the primary purpose of your job. Your job is now to ensure that others have the resources, environment and information they need to solve problems. You are a gap filler - and to do that you'll need to listen to your superiors and your subordinates to understand where those gaps are. It's just a change of focus.
Fix this first. It's a prerequisite for leadership.