Velcro's actually pretty easy, but I know it messes with people.
To be honest, I wind up doing velcro different each time, because I'm nuts like that. This is the general way that it gets done.
If you're working with a shirt, it's typically okay to leave the back flopping open. Anything else will need to be closed at the bottom. Pick up an AG dress and look at it: it's usually hemmed a bit under the velcro, and then sewn together.
The best velcro I've found is the very very flat generic "fashion trim" velcro. I can only find it at Wal-Mart. It comes in colors, but I usually just buy it in black. It's flat, so it won't mess with the fit of your project, plus, it's less likely to catch your doll's hair.
Don't buy the stuff with the sticky back! That's the very hardest to sew! I've sewn with it before, and I had to use pliers to get it stitched in.
You need to do this WITH THE DOLL YOU'RE SEWING FOR. Not another doll, not a model. That's the only way to guarantee that it will fit. I've handled a lot of dolls, and I promise they all have different waist lines. Put your project on the doll.
One side of the back of your piece should stick up and one side should stick down. American Girl usually sticks the up side on the right, so I do too. You can reverse it if you really feel like it.
Either way, fold the back edge of your project over twice, then pin the velcro on top.
Fold the other back edge of your project over twice, but this time, pin the velcro on the back over the fold.
Try velcroing the back up. If it doesn't fit, adjust the pins until it does.
Sew the velcro on. Sew around all four edges, like a box, and make sure to sew down the edge to tack the rest of the edge down. Like so:
That should be the last step, unless you have one final skirt seam to close. There you go, enjoy!