Dreamhost won't let you use webrick if you're using shared hosting. You can either use FastCGI or Passenger to host Rails on shared DH (mongrel is an option if you upgrade to DreamhostPS, but that's obviously more expensive).
For FastCGI, you will need a dispatch.fcgi file (older versions of Rails would generate one when you created a new Rails app, but that stopped around 2.2 if I remember correctly) as well as code in your .htaccess to send requests to the dispatcher. See the Dreamhost Ruby on Rails wiki page for details about setting up FastCGI.
The more preferable option is to set up your application to run on Phusion Passenger (aka mod_rails). It should be pretty simple through your Dreamhost panel, you just need to enable the domain to use mod_rails, and then set the directory for the domain to the public directory of your application. See the Passenger wiki page for more details.