Duplicate type layer with transparency

First time posting here, and I'm a newcomer to Illustrator from the After Effects world, so I'm sorry if this is the world's most basic question!

I'm looking to create (for lack of a better term) partial duplicate layers of text, offset from the main layer with transparency in between.

A common effect in vintage typography, as seen here:

http://www.vintageseattle.org/wp-content/uploads/2007/11/rainier_beer_ ad_01.jpg

I imagine it will take some customization of the paths, particularly in the case of how the word "Seattle" appears here.  But I basically need to figure out the best way to duplicate the layer and keep only the parts of it I want to keep as an accent "shadow"

Thanks