The first part is the trailer for a fixie feature from track bike legionnaires, MASH SF.
The second is a video by Bre Pettis. This instructional DIY video shows you how to build a single speed fixed-gear or 'fixie' bicycle. Using old parts, build a bicycle effective for flat grounds. It looks like a lot of work, but if you have the tools, it should be relatively inexpensive. Learn aside Bre Pettis and Make Magazine.
It's hip, it's cool, it can be made in a weekend. Look for a frame with horizontal drop outs (the groove where the back tire fits in) so you can tighten the chain.
Download the PDF for further instructions:
Watch this video tutorial and learn how to build a fixed gear bicycle.