I did it too as a kid. It gets easier every year with fewer connectors and more standard connectors. A computer is like a very expensive 10-piece lego. You just need to be patient and careful, and make sure to follow safety procedures (don't hook things up to power; ground yourself while working).
You have approximately the following components:
- Case
- Motherboard goes in the case
- CPU goes onto the motherboard
- GPU - entirely optional, both AMD and Intel chips have integrated GPUs - slots into a PCIe slot on the motherboard
- Power supply unit goes into the case, hooks up to the motherboard (and a couple other things)
- Disk goes into the case, hooks up to the motherboard and power supply
- Optional optical media player (DVD/BR player/burner) goes into the case, hooks up to the motherboard and power supply just like a disk
- Cooler goes onto the motherboard, over the CPU, to cool it (usually a fan)
- The case comes with fans, which need to be hooked into the motherboard too
- RAM plugs into RAM slots on the motherboard
- Optionally, a wifi card plugs into a PCI slot if you want wifi but you don't have it already on-board the motherboard
That's basically it. With adult supervision, your kid can put it together easily, and adult supervision only to make sure he doesn't plug power in until the whole thing is ready.
(Generally speaking, the only component requiring some strength is the I/O plate - this thing -
http://www.cybergooch.com/tutorials/images/buildsystem/IMG_6788.jpg - this tends to be a real pain in the ass to plug into the case properly. Of course it depends on the case.)