Like most of the writAARs, I use screenshots for everything. I tried writing on a pad, then using Notepad and alt-tabbing, but it was insane. Partly because I was insane (e.g. writing down the political %s every year in Vicky2 Ed - Who cared Me - I dunno, everyone? It's important! Ed - BZZZT WRONG! But thanks for playing). Now I have >3000 Screenshots in my HoI3 AAR, and they're already sorted, and if it matters, the date of creation tells me what session it was.
Keep in mind that the way you document your play depends a great deal on what the final product will be. My AARs have been almost 100% gameplay, just screenshots of what I am doing and short descriptions. So screenshots tell the whole story and I bring it together with text. Most players could skip the jokes and still get the story (Ed - but what about the dream sequence? Me - Ixnay on the Dream Sequence-ay).
If, however, you were going to do a story-based AAR, then you might want to go a different way. A notepad of some kind would be critical because the screenshot is no longer the story, it's just the inspiration for the story. I'm planning a CK2 AAR with more of a story to it, and my first abortive attempt showed me that I was going to have to go about things in a different way. The screenshots are part of the story, but they no longer tell you what the story is, they're just a place to hang your hat. Check out
Philo32b's Abyssinia AAR. Yeah, it's gameplay, but the story branches off the gameplay more like the one I have planned, and far more than my previous "I did this, then I did that" AARs.
My suggestion for anyone wanting to try an AAR for the first time, or try a new kind of AAR, is to to on purpose what I did accidentally. Start one, play a few AAR chapters worth, then write them up, expecting to trash the whole thing. If it flies, great, keep going. If it sucks, figure out how to do it better and start over (I'd also consider writing 6-10 chapters right at the beginning, AAR writing is more time consuming that it looks). My first attempt at CK2 was going to be 100% in character. I even debated not commenting as me or responding to comments so as not to break the spell (Ed - you're cute when you're full of yourself). Now, writing is risk, you can't always stay comfortable and sure of yourself, but the best way is just to test something and see what happens, like with the mushrooms you see in the woods or the cleaners under the sink.*
KiwiAssassin's way sounds perfect, you could spew out an entire story while the same is paused.
* - if you go out and poison yourself, don't come running to me.