Keep a diary!
From deadlines and lectures, to personal work schedules and university work, I keep everything in my diary, even personal things. It makes me very aware of everything I have coming up.
You should always take notes in lectures, but you should also be keeping those notes organised. You can either write your notes manually, with a pen and paper, or digitally - whatever works best for you!
The most important thing about staying organised at university is being proactive with assignment and deadlines. Check your module and course handbook, they will have information on when your assignments are due in.