I have a form with two inputs, user and password. How do I access these
two fields after a user fills them out and presses on the submit button?

I want to pass these two values to an action, add_user. How do I do

I have <% form_remote_tag :url => { :action => :add_user } do %>
        <%= submit_tag "Add user" %>
      <% end %>

A form submits its input elements. A form's input elements are the one it contains.

:add_user(a, b) doesn't seem to work

in the controller:
def add_user(a, b)

controller actions never take any arguments. The params hash contains the passed parameters. I reckon you'd safe yourself some time by sitting down with a decent book/tutorial.