I have built many computers over the years starting with a 386SX 16 Megahertz system back in 1992. It is a good learning experience to select and assemble the components of a computer.
However I doubt I will ever do it again. The reason? It is no longer cheaper to build a system rather than buy one off the shelf at Fry's or order one from Dell. The last few machines I have bought have been Macintosh's, so there is no possibility of assembling one of those. Also, the next computer I buy is likely to be a laptop rather than a desktop PC and those can not really be built by the home enthusiast. The last system I built was an AMD Athlon 1300 Mhz. I bought top quality components with an ASUS motherboard and an NVIDIA graphics card. I bought a Coolermaster case and 256MB of Crucial DDR RAM which was a lot back then.
At the time, in 2003, AMD machines were preferred over Intel based machines for their ease of overclocking the CPU for high performance. There is nothing particularly difficult in building a computer. Shops that sell the parts will help you with your selection of components. Take care not to damage the static sensitive parts is the only advice I can offer.
Building high performance gaming rigs is a reason why people continue to build their own machines in lieu of off the shelf HP or Sony models. I think just about anyone could build a computer especially if they have experience working with other mechanical or electrical projects. If you have the time and desire to learn about what makes a computer tick I recommend putting together your own dream computer before the art is lost forever.