I write things down as soon as I hear them, both in a notebook, I think it's a good idea to have one soly dedicated to the purpose of things you need to remember, or a daily planner if you will, that you can bring everywhere you go and as soon as I've done what I needed to do, I rip of a piece of the edge so I know approximately where I am. Another thing is before the week starts, to go thorugh the week to come and see when you have things planned.
Everybody has a phone, so why not use it? I usually sett alarms the day before I need to do something, writing a little text so I know what it's about, and one the same day a couple of hours before it happens.
Also, put up a list on your bedroom door of things you have to do for the day, or week, so you see it right before you leave the house. You can also use the help of others, ask your friend or someone you trust to remind you when there's things you have to do or tests coming up etc.
On another note, perhaps you could focus on improving your memory as well, there are exercises you could do and little tricks to learn to help remember.