Once the main box was built around the tundra, I started transplanting things from various places around Barrow into the Tundra Garden. I mostly focused on flowering plants. I tried to take mostly things from drier tundra, since the gravel pad under the garden meant that the drainage was better than most places where plants are right on top of permafrost.
Transplanting while in flower seemed a bit weird; that's not the usual method of proceding in more temperate climates. The growing season is so short here that by the time the ground is thawed enough to allow digging a decent size chunk containing the target plant, it's in bloom. Waiting until it was done means there isn't enought time for the plant to settle in.
I put a small pit in one corner of the garden and lined it with plastic under gravel and soil. I hoped that this would hold water in a bit and let me grow some of the flowers from moister parts of the tundra. In cases where I wasn't sure what a plant wanted, I'd scatter them through the garden a bit.