If you could offer one piece of advice for becoming a better manager, what would it be?

LISTEN. I learned this the hard way. As a new manager, I thought I knew it all and boy did that screw things up! Instead, take time to listen to your team and evaluate the situation from many angles. I found that even if I had to disagree with an employee if I listened to them first they were OK with the different direction. People want to be heard and valued. This is what separate the OK managers from the great ones.

Constantly be developing yourself as a person who inspires with choices that respect the people who work for you as much as the company. Be a person of uncompromising honesty, transparency, self control, ethics, humanity and wisdom.

Don't speak platitudes. Communicate to build relationships. Hold yourself to a higher standard than those you are in charge of. Commit to your own humility daily.

Be nice

I heard somewhere that "employees leave bosses, not companies" while I was in a job and this line changed me forever. Love your team like your family and they can get an even bullet for you.

My honest answer to this question based on my managerial experience is understanding and communication.
There was a time i asked my co-workers under me to do things, they grumbled and did that work in a bad way. i sat down and analyzed the situation. I had to put myself in their shoes and recalled how i had given out instructions.
Then i came up with another approach which is 1. trying to understand their feelings 2. communication.
The moment i understood them and was able to communicate effectively with them, there was no problem between me and them.
I got maximum result and my subordinates like me. Note that the kind of people i managed where older than i am and i was able to coordinate them well. In this part of the world age matters yet i am able to achieve results.
We now relate on personal terms like hommies. This has been my key in the different organizations i have worked. I trust this approach can give result anywhere since it can be effective in a country like mine in Africa, it can be effective any where in the world.
I hope this real case scenario is helpful to you.
thanks

Listen and LEARN, just because you manage does not mean that you are the expert in certain areas, in which your staff are most likely to be well versed within their roles. Listen, Learn and the Lead. Sometimes all they need is an ear to help then work through a object or issue.

Invest good time and effort in creating processes and trainings.

Listen to your employees! A great manager recognizes that they have just as much to learn from their employees as the employees have to learn from the manager.

Listen and delegate

Treat your associates as you would customers. Listen to them. Have a genuine interest when they come to you. Do not ask them to do something you would not. Share happenings and changes as soon as possible so your people find out what could effect their jobs and lives from you and not he "grapevine".