Its a little difficult to see, but this is the best picture i have of how i do the dividers. If you look at the side, you can see that the horizontal is joined to the vertical with a half-lap sort of joint. As far as how the divider is attached to the box, it isnt. The 2 long pieces are cut to fit perfectly inside the box, giving a decent friction fit, so the divider can be moved side to side, or removed completely. Personally, i think thats the better way of doing it, letting it float, but if i wanted to secure it it wouldnt take much, just a dab of CA glue. Doesnt require much strength after all, no need to make it complicated.
You could dado it in to be sure, but really, why bother?