The claw joint is one of the simpler joints out there, if you just want that to be opened and closed, you could potentially eyeball that joint. To make the other joints move, you'd need to carefully sculpt, mold, and then cast hollow pieces. In the traditional technique, you need to run a series of steel wires, pulleys, springs, and anchor points in such a way that the motion of your hand or arm causes the wires to retract or extend.
In Hollywood, when actors have wild animatronic appendages like this, they are very rarely operating them by themselves. They use camera tricks to hide the fact that there are a series of cables running down behind the actor connected to a box being run by one or more operators.
If you have money to burn, you could conceivably place a remote controlled electric actuator inside the claw. Since it would all be self-contained, you wouldn't need to run any cabling through the pieces. It would add weight, so the rest of the arm needs to be very rigid and strong and strapped to your shoulder, if not completely harnessed around your body.
You'd make the base of the claw hollow with a slot. You'd make the "finger" such that it has a wooden bar at the end. the wooden bar would go into the slot, and you'd use an axle to anchor it. The end of the bar is connected to the actuator. Assuming it's a linear actuator (a bar that moves back and forth), you just fasten the actuator housing to the far side of the claw and you're all set. If it's a stepper motor, then you need to set up a cable, a spring, and a pulley or two.
You can get RC actuators to do small things often by just tearing apart a cheap RC car toy. If clever, you could use the main motor of an RC car to do this. Otherwise, buying the component you need will easily run you $100 or more.
Oh, and one fun trick to make a hollow piece is to carve it from polystyrene insulation foam, paint that with gesso so resin won't dissolve it, then coat the foam in fiberglass+resin. Once the resin has fully hardened, drill a hole and pour acetone into the foam. The acetone will eat the foam leaving you with a hollow fiberglass shell. Naturally, this is a messy process and should be done outside with all sorts of proper safety equipment, and away from sparks and flames.