You sure can. Building a computer is not difficult, it just takes patience and some decent troubleshooting skills. Going this way can also be a bit less expensive since you are not paying a markup price for a complete PC. If you are really inexperienced, I recommend purchasing a ready-built computer by a reputable dealer, or even online. Again, we can help you with this to.
One of the first things to consider is purpose for the computer, and the second is price. What would you like the computer to do? We can help you spec' out the parts and find the sources for them.