I think the best way to teach your kids GTD is to model it for them. They need to see you doing it so that they can ask questions about it. You could start your child off with mind mapping. (One of the first processes that I learned) Introduce this as a way to remember things, and teach this along side making lists.If your child is young you could have them draw pictures to represent things, then gradually substitute that for words.
When I was little, my mom used to get a whole bunch of free calendars, and give them to us. We used to think we were so important using them and liked to ask her what would happen on such and such a date. Then we would fill them out with "writing" or pictures. You could use this as a way to teach some of the GTD methods. Sit down with them and help them fill out a calendar, explaining the process along the way. Hang it in their room and give them a pencil with which to cross out the days. As they get older this should become a habit for them.
Create a To Do list (Or chore list) with them. It would be best if you help them write it so they know the process.
As they get older introduce the rest of the GTD methods as ways to help them get done with school and chores, with the best results. And the best thing you could do is use GTD as a family.
Reading Wendy;'s remarks reminds that children will do more of what they see you doing than what they hear you saying.
I can certainly think of many areas in which I, as a parent, can improve. Still I see the value in modelling this in our home school activities. Hopefully, my children won;t have to struggle with the same organizational issues that have taken me years to overcome.
I wish my parents had taught me this stuff when I was a kid.