When you're bouldering, one critical part of this equation is not only the climber, but also the spotter. The spotter is the person in charge of watching the climber, making sure that they are falling in a controlled manner, really trying to do all that they can to avoid any injuries, awkward falls, things like that.
A couple critical techniques for spotting is going to be to make what Gaz is demonstrating here: having your thumbs tucked in, not out. Consider thinking about spoons, not forks. This way, you're going to avoid having those fingers get jammed if the climber comes down and you're trying to direct that fall.
So aside from the hand position, you're also going to be guiding the climber's hips. You're not trying to catch the climber, simply aid in that descent. So you're going to be standing and positioning yourself in a way that you expect the climber to be falling.
Right now, Gaz is on his cell phone. This is a terrible example of how to spot. He's not paying attention. He's not really doing anything but probably getting in the way, making a second victim here. Also, it's misleading to Tiffany, who might think she has an attentive spotter and it's just really bad etiquette. So if you ever see this happening, certainly step in; stop that.
If you see someone climbing without a spotter, don't hesitate to get up and spot them. If you're climbing and you don't see someone available to spot for you, don't hesitate to walk to the front desk, find a staff member that might be available, or ask someone that might be in a different section of the gym if they could come over and provide a spot for you.
So remember, keep those thumbs in. Try to look for the direction of the fall. You're directing a climber's hips, not trying to catch them. And those are some basic principles for how to spot in a climbing gym.