Rails route for button - ruby-on-rails

Question

I'm a rails newbie and a question on routes is confusing me.
On one of my pages, I have a form. In that form I allow the user to fill in some needed information and press a "submit" button.
I get:
No route matches {:action=>"inventory_test", :controller=>"test_types"}
I do have an action in the test_type controller for "inventory_test".
My confusion is that routes seem to be defined according to the REST model, such as /Users/edit/1. That's fine, but how does one create routes for things like buttons?
I may be naive, but it seems like if I tried to setup a route in the form:
match 'some/url' => 'controller#action'
then I'm essentially defining the action for the entire page. How do I define actions for elements on the page?
When this button is clicked, I want the action in the controller called. I'm looking for:
match "submit_button" => 'test_types#inventory_test'
I realize I'm likely misunderstanding the paradigm, so any education is greatly appreciated.
Code:
(Note that I haven't tested the form code yet, but hopefully you get the idea)
index.html.haml
%div
%table
%caption
Inventory Tests
%form
Inventory Run: %input {:type => 'text', :name=>'inventory_run'}
Inventory Class: %input {:type => 'text', :name=>'inventory_class'}
=button_to "Run Inventory Test", :action => 'inventory_test';

Answer 1

If you are submitting a normal form then this should help
The route match '/url' => "test_types#inventory_test" should work fine.
<%= form_for(#user, :url => "/url") do |f| %>
"Put your form code here"
<%= f.submit "Submit" %>
<% end %>
Revert back if any queries .
Edited as per code posted
%form{ :action => "inventory_test", :method => "post"}
%label{:for => "inventory_run"} Inventory Run:
%input{:type => "text", :name => "inventory_run"}
%label{:for => "inventory_class"} Inventory Class:
%input{:type => "text", :name => "inventory_class"}
%input{:type => "submit", :value => "Submit"}
Just check, it should work for you but i have not tried with it