There are two ways to do this trick. One requires a cushioned table top (like in a casino). When the table has cushioning, you can push down on the side of the chips, to force the other side to go up.
The second way, you have to pull the chips up with your finger. My video shows this second method, because you can use it on any playing surface.
The more chips you use, the cooler it looks, but the harder it gets.
You might find helpful to use your pinky too, to keep the chip stack lined up.
Certain poker chips make this trick more difficult. I've found that the cheap "diamond" chips are hard to shuffle, because they have a deep ring cut into the surface of the chip. Also, it's easier to this trick with old, worn-down chips, because they just seem to slide into each other automatically during the shuffle.
The hard part, for me, was to keep the thumb-side stack from tipping over to the side. This is because you only have one point of contact on it (thumb). The key is to make sure that stack stays completely straight, on your thumb. The other stack is easy, because you have several points of contact to keep it straight.
Once you’ve got to where you can to stacks of 3 pretty consistently, move up to stacks of 4, 5, 6. I usually do stacks of 6 (12 chips total) when playing at a $3/6 table, and I do stacks of 8 (16 chips total) when I’m sitting at a $4/8 table (so I can quickly grab the proper bet amount).