Before you can use the Kodi Remote you have to verify that a couple of settings are enabled in Kodi.

Go to "System -> Settings"

And then select "Services"

Webserver

Select Webserver in System -> Settings -> Services. The following options can be configured on this screen

"Allow remote control via HTTP": You have to enable this option to be able to connect to Kodi
"Port": Set the port number under which the Webserver will be listening. Default port number is 80 or 8080 depending on the operating system.
"Username & password": You can optionally set username & password
Remark: Setting a password is not required and does not provide good security since the password is sent in clear text. Do not make this port available from the internet!

Remote Control

Select Remote Control in System -> Settings -> Services and enable the following two options

"Allow remote control by programs on this system": Enable this option. Enabled by default
"Allow remote control by programs on other systems": Enables the remote to receive playback notifications
Remark: If you forgot to enable this option you will still be able to browse your media library and start playing files however music playback will probably stop after playing one song and the status of the currently playing file won't update properly.

Zeroconf

Select Zeroconf in System -> Settings -> Services. This step is optional but will allow Kodi Remote to automatically detect and configure your Kodi mediacenter

"Announce services to other systems": Enable this to make Kodi discoverable on your network.
Remark: If you try to enable this setting on windows it will fail if Apple Bonjour is not installed. It comes bundled with iTunes or can be installed from http://support.apple.com/kb/DL999

UPnP

Select UPnP/DLNA in System -> Settings -> Services.

"Share my libraries": Enable this option to share your media collection over UPnP. This option is only required if you have set username & password in the Kodi Webserver

Find your mediacenter IP address

Go to "System -> System info"

And then select "Network"

The IP address is the value after "IP address"