Once the dome mold is set up, it's just a matter of setting the rest of the bricks in place. I kept going in concentric circles, setting each brick in place as I went.
When I got to the last few bricks, I had to knock a few edges off them to make them into wedge shapes so that they would lock together to support the dome. Then it was just a matter of getting as much mud in between them as I could to fill up the gaps.
I'll leave the mold in place overnight to allow the mortar to set the bricks nice and firmly in place.