So, here's how I fixed it:
First, I made sure all my resources were defined in the routes
file.
resources :groups
Second, this is how I figured out the link_to
method:
<%= link_to group, method: :delete, class: 'btn btn-danger', confirm: 'Are you sure?', :remote => true do %>
<i class="fa fa-trash-o"></i>
<% end %>