I highly recommend etching a PCB for this project. They are more resilient and reliable than perfboard (IMO) and therefore more suitable for use in a childrens toy.
Start by etching your board using your preferred method. I won't go into detail here - check out my other instructable on how to use the toner transfer method to make a PCB.
Now, populate the board using the parts list and board layout as a guide. Start with the ICs, and then the resistors and caps. Make sure the two electrolytic capacitors are installed with the correct polarity. When soldering the LEDs, bend the leads a bit so that the LED is flush with the edge of the board. LEDs are polarized too, install the the right way! Finally, solder in the potentiometers and the 9V battery clip.
Two of the switches will have three wires, one of them only needs two. Solder about 2-3" of wire onto the pins of the switches, and finish them with heat shrink. Note that the body of the switch must not be longer than the standoffs, or they won't fit!
Cut a piece of perfboard equal to the size of the PCB (3x3 inches). Drill holes in the four corners that match the holes of the PCB. Drill three more holes that match the shaft diameter of the switches. You can put these three holes wherever you like; I chose to put them in a line. Mount the switches on the perfboard, using one of the supplied nuts. Save the second nut for later.
Now it's time to solder the switches onto the PCB. Match up each switch to a position on the PCB, and solder its wires in place. Make sure that the middle pin on each of the switches with three wires goes to the middle pin on the PCB. Soldering can be tricky, since you have to solder to a pad on both
sides of the board.
With the switches installed, you may link the perfboard to the PCB using the standoffs. The perfboard should be mounted as shown in the picture. I used flathead screws on the perfboard side, so that the screw heads wouldn't cause the fabric to bulge. Don't tighten the screws completely just yet though, as you'll need to remove the PCB from the perfboard for mounting inside the robot's head later on.
Solder long wires to the leads of the photocells, and finish the joints with heat shrink. You may also want to add a glob of hot glue to where the leads connect to the package of the photocell for added strength.
Finally, solder long wires to the speaker terminals and finish the joints with heat shrink.
Don't solder the photocell or speaker wires to the PCB yet - you need to mount them inside the Thingamaplush's body first.