First, use the USB MIDI of the Komplete Kontrol keyboard. Connect the USB from the keyboard to your computer.
Secondly, please read these articles for setting up External Midi Devices with Studio One 3, this covers the basics and gives a basic over view of setting up MIDI devices:
Then, the following information pertains to Komplete Kontrol specifically.
1. When you go to Options > External Devices in Studio one, you add the New Keyboard, and then put the MIDI Send To and Receive From through Komplete Kontrol Port 1. This controls the keys.
2. When you add the New Control Surface, you put the send through Komplete Kontrol DAW 1 and leave Receive From blank.
3. With those settings you should be able to use it as a MIDI controller and also integrate the Komplete Kontrol software for instrument tracks.
Here is a YouTube user showing how to setup NI Komplete Kontrol:
Please keep in mind, we don't have the Komplete Kontrol here, so the above information is the best we can offer without the board. If the above information doesn't help, please start threads on the Native Instruments forums and Studio One forums for community help.