Getting to Kota Kinabalu is pretty straightforward. Close to the city is an International Airport (BKI), with flights to Peninsular Malaysia, Singapore, Japan, China, Hong Kong, Thailand, the Philippines and a few other Asian countries. If you want to fly to KK from Europe or America the best option is to fly to Kuala Lumpur or Singapore, and take a low cost flight to KK from there.
From KK you can take local flights to Sandakan, Tawau and Layang Layang (in Sabah, East Borneo); to Kuching and Miri, (in Sarawak, West Malaysian Borneo); and to Brunei and Indonesian Borneo. If you don't want to fly, you can also take buses to the mentioned destinations.
KK also has one of the biggest ports in Borneo, regularly visited by cruise ships.