Jansen Jones, Rob Romero and Optics Planet have done a great job of producing two videos that take you through building your AR15. Building your rifle is a topic misrepresented by the Gun Control Lobby. The core of the AR15, whether you are building your rifle or buying it as a complete system, is the lower receiver; as such, it has been defined by the BATF as a firearm and bares a serial number. Purchasing a stripped lower receiver is NO DIFFERENT than purchasing a complete firearm; it must be done through a federally licensed dealer who will collect a Form 4473 and run a background check to complete your purchase. All other parts may be purchased over the counter or from your favorite retailer.
The principal reason for building your own rifle is first and foremost to customize your weapon with the myriad of accessories that are available; generally, all your competition guns are built from the ground up. Other reasons include cost savings or just plain fun.
The videos below take you through a complete build in structured and easy to understand presentations.