If you want to go to Nusa Penida Island from Bali, the easiest and cheapest way, if you go from the capital, Denpasar is by getting to the Sanur beach and using some traditional public boat called 'jukung'. Jukung will cost you maximum around IDR. 40.000 and it will take around 90 minutes to reach Nusa Penida.
There's another option you can take if you go from Sanur. You can also take some speed boat which is a lot more expensive than jukung (could be IDR 50.000 more expensive) but also a lot more faster (50 minutes). If you want to travel with your own car/ motorbike to Nusa Penida (please noticed its only for Nusa Penida, not Nusa Lembongan and Nusa Ceningan) you can go Padang bay (on the east part of Bali,an hour drive from Denpasar) to take a ferry boat (Kapal Ro-Ro and Kapal Re-Re).
This boat will take you crossing the Badung Strait, and the trip will take around one hour to get to the Toya Pakeh Harbor in Nusa Penida Island. Beside from Padang Bay and Sanur, you can also take some jukung from Kusamba (cost you around Rp. 25.000).
There are public boats from from Sanur, Kusamba or Padang Bai in East Bali.
From Padang Bay
You can catch the daily public ferry (large boat that includes vehicles). A passenger ticket is approx Rp 16,000 each way. There is also a smaller public ferry speed boat service that typically carries up to 20 people. This departs from Padang Bai beach side every morning. You should be at the beach side by 6:30AM to catch the public speed boat. Buy ticket from ticket office near beach and then wait until the boat has enough passengers for the boat to depart. The ticket cost is about Rp 40,000 each way.
From Benoa Harbour
Quicksilver  Runs daily cruises from Benoa Harbour in Bali to their monstrous pontoon which floats off the north western shore of Nusa Penida. The trip includes watersport activities centred on the pontoon. Rp 570,000 per person.
Caspla Bali Boat, Sanur Beach in front of Ananda Beach Hotel, ? +62 361 7912299. Speed boat service, 3 times daily to Nusa Penida. Scheduled departure from Sanur Beach at 11AM, 2PM and 4:30PM. Departure from Buyuk, Nusa Penida at 8AM, 12:30PM and 4PM. One way fare Rp 200,000/person and return Rp 400,000/person.
Maruti Express, Sanur Beach in front of Ananda Beach Hotel, ? +62 819 1626 8871. The first speed boat service to Nusa Penida. Scheduled departure from Sanur Beach at 10AM and 4PM and departure from Nusa Penida at 9AM and 3PM. One way fare Rp 250,000/person and return Rp 480,000/person.
From Nusa Lembongan
Public boats depart daily at 6AM close to the suspension bridge between Nusa Lembongan and Nusa Ceningan and run to Toyapakeh or Buyuk Harbour in northern Nusa Penida. There are also services from the Jungut Batu area of Nusa Lembongan to Nusa Penida. All of these can be a little 'worrying' at times and are often very crowded.
Charter boats are available, departing from and arriving at the same area as the public boats. If you are staying on Nusa Lembongan, ask at your hotel. If not, go to the shoreline close to the suspension bridge or to the beach at Jungut Batu and ask around amongst the boatmen. Rates certainly vary but expect to pay around Rp 300,000.
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