I've only started getting somewhere with being organised in the last couple of years since having two calendars - one by my desk, and one on a pin board I have next to the kitchen. I write down birthdays and term dates soon as I get the calendar, and also bin/recycling days, pay days, and days bills are due go on it straight away.
Appointments go on soon as they are made and I check it each day while I'm waiting for the kettle to boil.
I also make a point of crossing off each day with a big fat line so that I know where I am
The calendar by my desk is just a small one and I write the initials of things happening on it, eg rent due would be R, child benefit going into my account marked as CB, Doctors appointment DR, birthday as BD - then the actual 'thing' that is happening is written properly on the big kitchen calendar. This is because I sit at my desk a lot, so see it a lot and can depend on it to make me look at the bigger calendar and see whatever it is happening that day just in case I've been side tracked in the morning and not looked.
Post I deal with soon as it arrives and bin/recycle the junk and put anything important in my in tray which then gets looked through and sorted and filed away twice a week ish.
DD is responsible for her own organisation, with some pointers from me along the way about keeping tidy, and working out when she needs to be studying or doing homework and when she will have free time.
I also try and make time count for double so if I need to nip into town to buy a gift or post a card and know i will be running out of allergy meds, something else needs paying/posting/picking up/paying into my bank etc, I get everything done in one trip
If I'm going into the kitchen/bedroom/bathroom I take something with me that also needs to go there, cups into kitchen, DDs bloody hair bobbles back upstairs etc
I load the dishwasher and feed the cats while waiting for toast to pop up or kettle boiling
Hoover or quickly clean kitchen while I'm running a bath
Shove something for dinner in the slow cooker while making lunch or packed lunches
I shop online because it saves me tons of money and time
If I have a week or a day with an unusual lot of daunting tasks, or a lot to remember I make a list and keep it on my desk crossing off as I go
cripes I had no idea I actually did all this til I wrote it down!