I have a method that I follow religiously to get things done, and it doesn't really have anything to do with time management.
See, time management is a misnomer. Time does only one thing: it marches on. So, instead, you need to manage your priorities.
Here's what I do: at the end of every day, I write down the three most important things to do the next day, and then, when I start working the next day, I work on those three things before doing anything else.
That way, my priorities dictate my time.
One of my direct reports came to me during onboarding and asked how to prioritize her schedule. When the number of things on your to-do list outpaces the number of hours in a day, follow the ABCs:
These are essential to your job. They're the things you were hired to do, and they need to be at the top of your mind. Do the things on your A list before anything else. Make time every day to work on these.
These tasks are tangentially related to your job. They're typically on someone else's A list, so they seem urgent, but make sure you do these after your A list is complete.
These are tasks that you finish when you have time. They're often the "fun" items. The dreams for the future. The someday list. Work on these, but only after you've worked on your A list and B list in a week. If you prioritize these, you'll fall behind and it'll seem impossible to keep up.
Don't let your time be prioritized incorrectly and therefor ineffective for your responsibilities and duties. Ensure your day is best structured according to your priorities, and you'll see that you're accomplishing the tasks most urgent in an efficient manner.