Oh I've sort of done this a little...
Um here is what I think it is.
Basically your child is mostly about feelings, adult is mostly your internal sort of life guide (and conduit of change), and your parent is stuff you learned from when you were young (were taught about life).
Inside it works like... let's say you feel like watching a silly tv show, and in your head you're hearing "you're so lazy, you shouldn't be watching tv when there are dishes to do". That's your child/parent side in a conflict (if your parents taught you that relaxing was bad, for example). Or let's say you've had candy for dinner the last 3 nights in a row, and you think okay I really want to be healthy so... I'll have an apple with my candy and see if I can get back to normal food (if you have no pre-taught stuff about not eating candy for dinner) that might be more like your child:adult interacting.
It's sort of... I think like the adult is an objective observing self, the parent is like past attitude and the child is reactions. It's hard for me to articulate because in my therapy/mind I use different and more words to describe this since I have several of each part - they come from the same "ego state" but they are only one slice of ego-state pie I've got going on.
When you look at it on the outside rather than the internal examples I gave it's.... who you are reacting to in another person, and how they are reacting to you. So... you could have a business interaction w/ someone at work in a meeting those are usually adult:adult type things (they generally end up child:child haha, but let's say you don't work at my company...). Or if you're scolding someone, like telling your H "wtf man you can't organize the dishwasher at all don't you know cups go on the top!?" and your H feels super small or like you hate him or something that could be a parent:child interaction. If you and your friend are laughing at a fart joke that's probably a child:child interaction. But it's way more complicated than that and I mean all my examples are open to interpretation, I don't think anything is hard/fast or set in stone.
Just back on the internal thing for a second, I use TA to self-sooth and calm. So let's say I'm all butthurt over something or I have anxiety that's more of a child part, and then my adult self takes care of me by either feeding me (usually if I don't eat I get anxiety naturally), or doing something else. If I start beating up on myself for feeling something... that's my internal parent being a jerk. And then if I have problems like... I shouldn't go back to school to be a ______ because ________ is not something I deserve to be that's my adult self and my parent self at war... In my therapy we work primarily on the inside.
Anyway.... so that's my uneducated stab at an explanation.
So how you may act them out in a week could be if you have over-exaggerated reactions that could be a child part thing, if you're beating yourself or others up and judging and it's related to stuff you learned growing up that's maybe the parent, and then if you're cooking dinner, making a schedule and generally living life between (even the observing of your ego states counts) that is your adult self.
