We've previously covered DIY bicycle panniers, but they usually require your bike to be fitted with a cargo rack. If you don't have one, you can use PVC pipe and fittings to support a milk crate.
Instructables user bonedoggie needed a basket to transport vegetables and used a PVC pipe to build a frame to hold the milk crate. His bike had an unused hole drilled by his rear axle, so he drilled holes in the PVC to attach and built a frame to hold the milk crate. This seems to be a great way to add cargo room to a bike on a budget.
PVC and Milk Basket Bike Basket [Instructables]