date_field()
is a new helper in Ruby on Rails 4.0, so you're probably using an older version like 3.2.13.
These are examples of the form helpers available in Rails 3.2.13:
<%= text_area_tag(:message, "Hi, nice site", :size => "24x6") %>
<%= password_field_tag(:password) %>
<%= hidden_field_tag(:parent_id, "5") %>
<%= search_field(:user, :name) %>
<%= telephone_field(:user, :phone) %>
<%= url_field(:user, :homepage) %>
<%= email_field(:user, :address) %>
And you can find the documentation of this here: http://guides.rubyonrails.org/v3.2.13/form_helpers.html#other-helpers-of-interest