You will need to change a few things:
You'll have to pass the title
attribute to any paths/urls when you do stuff like link_to
e.g.
post_path(@post)
will become
post_path(@post.title)
You'll also have to update your finds to look for posts by title, as opposed to id e.g.
@post = Post.find(params[:id])
will become
@post = Post.find_by_title(params[:title])
That should get you started :). You'll obviously want to slug the title and validate the uniqueness of the title as well.
EDIT: After reading Robert Elwell's answer, maybe I misunderstood the question. Do you already have a route like you described for a specific object, or are you doing this with the 'basic' routes? If the latter, you're much better off writing a custom route like Robert suggests, and then doing some of the stuff I suggested.