In high school I kept all of my homework and due dates in a leather planner. It worked well. But in college I moved everything to Google Calendar. Each week I would take the homework due in all of my classes for the next week and put it into the task list. So, for example, for Interactive Journalism, when I had a blog post due, I would write IJ Blog Post 1. I went through the syllabus and kept a few major assignments towards the bottom of the list so they were always somewhere in my mind.
That was how I stayed on top of my homework in college. I also took to writing down what I wanted to accomplish each day, and each day of the weekend. When I was really on top of it though, I would work over the weekend to work on the whole next week's homework. Sometimes I finished, sometimes I didn't. But it was a great feeling to have all the homework done for the whole week.
Sometimes, when I couldn't do it all over the weekend, I did the day it was "assigned." So after Monday's Interactive Journalism class, I would do the homework due for Wednesday's class.
And at the very least, I would do the homework the night before. I don't think that I ever the did the homework the morning of except for once or twice. It's not worth it.
What I originally tried to do was to start homework on Friday afternoons so I could have Sunday's off. But what my friends would do was save their homework for Sundays. And it's not much fun to do homework while your friends are hanging out, or, alternatively, to have free time while your friends are frantically studying. So I fit my schedule to theirs and saved my homework for Saturday mornings and Sundays.
With all of this, I was able to stay on top of my homework,
Hope some of this helps you out with your homework!