Hello Ricardo
Let me divide your task in 3 parts:
1. Decide what web framework to use. In Ruby, the most popular by far is Ruby on Rails. I would recommend to go with that. Another option is Sinatra, and there are probably others as well.
2. Extract image (and possibly other information as well) from the DICOM file.
This is where ruby-dicom is used, e.g.:
dcm = DICOM::DObject.read('file.dcm')
image = dcm.image
image.write('dicom.jpg')
3. Display your dicom-image in the web page. In Rails this is handled with code in your controller and view. This is a straight Rails-problem (i.e. not related to ruby-dicom). I don't have an existing project or tutorial on this, so I can't help you any further, but it is not difficult to find this information elsewhere. Note that in Rails you are not forced to save to an image file before displaying, it is also possible to transfer the image information in memory to display it in the view.
Best regards,
Chris