I have no idea if this Blog gets much traffic these days. But a few people found the FastRWeb "howto" to be helpful, so I'll try again.
Working with graduate student Xiaofei Wang, we compiled a "howto" for the use of Amazon EC2: using Ubuntu, and installing Apache, R, FastRWeb, and Shiny server. The write-up and associated scripts can be found at http://www.stat.yale.edu/~jay/EC2/. All of this information can be found elsewhere in bits and pieces, but we've found it helpful to put this pipeline in writing.
Of course, you could try to rely upon images (AMIs) built by others. There may be some security risks, though, and it isn't terrible to do it on your own.