The easiest way is to use a web form to generate random integers (with duplicates, like dice rolls), randomized sequences (without duplicates, like lottery tickets) or raw random bytes. You can also flip virtual coins and generate random bitmaps.
Random.org was built and is being maintained by Mads Haahr who works as a lecturer in the Distributed Systems Group, Department of Computer Science, University of Dublin, Trinity College in Ireland.
All numbers are tested statistically and the results available in real-time. A comprehensive analysis was conducted in 2001. People have asked if there were anomalies on 9/11. The FAQ answers other common questions.
If you need many numbers, download the pregenerated files or write your own client to access the server via HTTP, SOAP or CORBA. Source code for a number of clients is available from the client archive. If you do this, please read the guidelines for automated clients.