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I tend to write as I play, which is partly why it takes me so long to do an AAR. I know, it's not the most efficient way of doing things...

Generally, when I get to an event I think would be interesting, I will CTRL+Print Screen then paste it into word, crop it/edit it accordingly, write my passage for it in the forum, add the pic and then continue playing, repeat as required. On occasion I will save a word doc with some flavour text and screenshot to write it up afterwards, particularly if I'm exploring something a bit interesting that could swing either way/make me revert to an earlier save (such as opening the L-gate and unleashing death upon everyone...).

As I say, it is not the most efficient and does take away from the gameplay a little bit. I'll probably look at doing something similar to what others have suggested here
 
The honest truth of the matter is there's no one good way to do it, you need to develop *a* system and then try to stick to it, because otherwise you go crazy.
Like others, I use F11, which auto generates a screenshot with the date and a serial number. I hit the button frequently anytime I *think* it might be interesting.

At the end of the session I go into the screenshot folder, create a folder called "Session 1" and dump all the screenshots into it.
If I play a second or third session (I try not to play *too* far ahead of my AAR's or I lose the thread) I likewise dump them into those folders.
Shortly after organizing them into session folders, I browse through them, thinking over the game session and create a sub folder to put them into whatever categories make sense.
In Stellaris, for instance, I have a folder for selected traditions, a folder for combat, a folder for anomalies (which contains both the anomaly found screen and the result), a folder for alien contact/communication and so on.
I make sure when I "use" a screenshot to put it into a folder for used screenshots. In past AAR's I've deleted used screenshots and regretted it sometimes because I ended up wanting to use them again in a different way, so now I make sure to just get them out of the way by putting them in the used folder.

I personally find a wall of screenshots almost impossible to process so its important for me to break it down into smaller batches to make it sensible for me.

And yes, before you ask, this does require some work, but I find it less work than trying to find and keep track of hundreds of unorganized screenshots, and so...