Twist the thread by rolling it several times between your thumb and forefinger. You should see the beads start to twist around each other when you lay the second set of beads down against the first. Do not let go of the thread as you secure the fringe in the next step - if you do, the twist may come undone and the fringe will not twist.
As you work, the thread will twist easier. For this reason, I usually recommend using a nylon-based beading thread such as Nymo or Silamide when working twisted fringe.
This is the trickiest part of working twisted fringe, but it does get easier as you practice.
