The two main entry points are Broome in the west and Kununurra in the east, both with airports served by Qantas and Virgin Australia from Perth, and Kununurra also from Darwin. Broome connects the Kimberley to the rest of the coast; Kununurra is the eastern gateway and the base for the Bungle Bungles.
Driving to Broome from Perth is about 2,200 km along the Great Northern Highway — a two-day drive minimum, though most people break it into three or four days if they're stopping along the way. The road from Darwin to Kununurra is about 830 km via Katherine. Both routes are on sealed roads and accessible in a conventional car.
Once in the Kimberley, a 4WD is required for the Gibb River Road, Purnululu access road, Mitchell Falls road, and most other roads away from the sealed highway. Car hire in Broome and Kununurra includes 4WD options; prices are high, especially in peak season. Ensure any hire vehicle is genuinely capable — the creek crossings and corrugations of the Gibb River Road are not appropriate for underpowered soft-roaders. Many people fly between Broome and Kununurra rather than drive the full Gibb River Road and return, using one as a starting point and the other as an endpoint.