Rewritten; added usage example for request specs.

Changes

-Do it like this in your controller specs:
+The Basic Authentication header encodes username and password. Effectively, it's just Base64 plus a "`Basic`" prefix.
+You can use `ActionController::HttpAuthentication::Basic.encode_credentials` for that, and put its result into the `Authorization` request header.
-    credentials = ActionController::HttpAuthentication::Basic.encode_credentials 'alice', 'secret'
-    request.env['HTTP_AUTHORIZATION'] = credentials
-    get :index
-    # ...
-You may want to add `spec/support/auth_helper.rb`
+## Request specs
-    module AuthHelper
-      def basic_auth(user, password)
-        credentials = ActionController::HttpAuthentication::Basic.encode_credentials user, password
-        request.env['HTTP_AUTHORIZATION'] = credentials
-      end
-    end
+For request specs, use the `:header` option.
-and `include AuthHelper` to the corresponding specs.
+```ruby
+it 'requires authentication' do
+  get '/'
+  expect(response.status).to eq(401)
+end
-Your specs will then look prettier:
+it 'accepts valid credentials' do
+  encoded_credentials = ActionController::HttpAuthentication::Basic.encode_credentials(username, password)
+  get '/', header: { Authorization: encoded_credentials }
+  expect(response.status).to eq(200)
+end
+```
+
+
+## Controller specs
+
+In controller specs, you can put then into `request.env['Authorization']`.
+
+```ruby
+it 'requires authentication' do
+  get :index
+  expect(response.status).to eq(401)
+end
+
+it 'accepts valid credentials' do
+  encoded_credentials = ActionController::HttpAuthentication::Basic.encode_credentials(username, password)
+  request.env['Authorization'] = encoded_credentials
+  get :index
+  expect(response.status).to eq(200)
+end
+```
-    basic_auth 'alice', 'secret'
-    get :index
-    # ...