Greyhound Australia has a regular service to Monkey Mia via Overlander. If you're coming via Denham, the Bay Lodge shuttle runs to/from Monkey Mia.
Skywest Airlines has four flights per week leaving from Perth's domestic terminal. Flights get into Shark Bay airport and a transfer service to Monkey Mia meets all commercial flights for a small fee.
Cars can be rented in Denham at Shark Bay Car Hire and there's also a local taxi service, SWAT taxi, that can get you around.
Monkey Mia Wildsights offers limousine tours of the area.