If I understand this properly, you want to initiate an AJAX request and then update part of the page with a partial? If so, this is what you would do:
# html page
# (remote: true marks this link as an AJAX link)
<%= link_to "AJAX request", url_path_you_want, remote: true %>
@name = "Bob Smith"
# partial: _partial_name.html.erb
<%= @name %>
# view: action_name_to_match_your_path.js.erb (important to have .js.erb portion)
# (assumes you're using jquery)
This code will replace the innerHTML of the #content div with the text "Bob Smith", which is the contents of the partial file. I wrote this off the top of my head, so if it complains about unknown variables in the partial try "name" instead of "@name". I can never remember whether it's local or class variables in there.
Another approach is having the server just send back a message (via JSON or something) and then having the browser execute select code based upon success or failure. I think that's much more complicated, IMO, and the above approach is much cleaner.
I can't take credit for this concept; Ryan Bates (of Railscasts.com) is where I first saw this employed.
Hope this helps!