Well, how do you remember stuff without writing it down?
Just just do...
If you're a quickly-distracted mind by nature, then that is not your fault, it's your parent's for not helping you with it.
Anyways, some commonly used "games" to remember stuff are:
-> Give stuff you need to remember a "place" in your house.
In other words, if you need to remember to "call your dad about something", then imagine a cellphone lying somewhere in your house. Whenever you then "think" about your house (which is the place you come most often), you then recall the cellphone, and should also recall the fact you have to call your dad.
-> Give it a more important meaning.
If you have to "call your dad about something" (Insert whatever), make it extremely dramatic, but believe it aswell. Or atleast get into the situation.
If you DON'T call your dad this weekend, he'll die...
Stupid stuff like that atleast get you on track.
At the end of the day, you can't "improve" your mind, or not in a conventional way. There is certain professional mind tests you can take, but they can only do so much.
Your best bet is simply, as said before, having a pocket-diary and writing everything down.
I also read that eating alot of FISH helps increase the brain capacity. (Don't expect miracles tough)