I had a really hard time getting it right consistently so I simplified it and it works now every time! Here's how I do it:
First, you take your two ends and hold them together. The pink yarn is what I'm joining to the green yarn...
then, wrap the pink yarn around your thumb ONCE. (In the video she has you wrap your thumb twice)
then wrap the pink yarn in front of the ends ...
fold the ends over the yarn you just wrapped in front
hold the ends snug against the tail of the green yarn. Slip your thumb out of the loop.
hold the ends snugly with the green tail then start to pull the pink yarn, (so this is obviously a bad picture because I don't have a good grip on the green end...)
make sure the pink loop stays down around the folded over ends
snip the ends and it's all done!