Long gone are the days of a separate application to control Keynote presentations from iOS. Everything you need to create, edit, present and control presentations is now contained within the Keynote iOS application. Here’s how to use the iOS Keynote app to control Keynote running on your Mac.
Keynote Remote Preferences
On the Mac select Keynote > Preferences and click Remotes to open the Preferences panel for remotes.

Keynote Remotes Preferences Panel
Remotes are not enabled by default so to ensure you are able to control Keynote via the iOS app be sure to tick the Enable checkbox (1).
Once connected the name of the iOS device will appear in the list on the right (2).

Run Keynote on an iOS Device
Open the Keynote app on an iOS device and tap the Remote option in the top left corner (1).

Keynote Remote
Tapping the Remote option opens the first screen of the Keynote Remote connection process.
Tap Continue at the bottom of the screen (1).

Set Up Remote
The second screen of the Keynote Remote connection process gives instructions on how to prepare the Mac version of Keynote to be able to connect it with the iOS device.
It also puts the iOS device in connection mode.

Link Keynote to the iOS Remote
Back in Keynote for Mac the name of the iOS device in connection mode will appear in the list on the right.
Click "Link" to link Keynote for Mac to the iOS device (1).

Passcode Displayed on Keynote
A passcode is displayed on the Mac running Keynote.

Passcode on iOS Device
Check the same code is displayed on the iOS device.

Passcode on the Mac
If the passcodes match click the Confirm button on the Mac.

Ready to Control the Slideshow
Once the Play screen is displayed you are ready to control the slideshow running on the Mac from the iOS device.

Confirm the Connection
Once the connection is made the Link button becomes an Unlink button in the Remotes tab of the Preferences Dialog Box.
Should you wish to unlink the iOS device from the Mac click this button.

Connected
Once connected the presentation open in Keynote on the Mac appears on the iOS device in presenter view.

Layout Options
There are several alternative layouts available from the Layout Options button at the top of the screen on the right (1).

Layout Options Screen
Tapping the Layout Options button opens the Layout Options screen.
The five alternate layouts are listed. The layout option currently selected is indicated with a blue tick.

Keynote Remote on iOS – Horizontal View
I find the most useful layouts to be Current and Notes, here shown in horizontal mode.

Keynote Remote on iOS – Vertical View
This is the same view, Current and Notes, in vertical mode.

Navigating Using the Keynote Remote on iOS
Swiping the slide to the left moves the presentation on to the next slide (1).
Swiping the slide to the right moves the presentation back to the previous slide (2).

Annotating Slides with Keynote Remote
The slides displayed on the Mac can have annotations added directly from the iOS device using the Annotations tools.
Activate the Annotation tools using the Annotate icon at the top of the iOS screen (1).

Annotation Tools
A range of annotation tools are shown at the bottom of the screen. The green pencil is selected here (1).

Managing Annotations
Annotations are made using your finger on the screen (1).
They can be undone using the Undo tool (2).
You exit annotation mode by tapping the Done button (3).

The Laser Pointer
Another tool available is the Laser Pointer tool.
This is accessed using the tool selector at the bottom of the screen (1).
The Laser Pointer is moved around the slide using your finger (2).

Stopping the Presentation
To close the presentation on the Mac you are controlling with the iOS device tap the cross in the upper right of the iOS screen.

Resources
Keynote for Mac is available from the Mac App Store.
Keynote for iOS is available from the iOS App Store.