Pengerang is an area at the southeastern tip of Johor, to the south of Desaru. The name is usually used to cover the dock and immigration post at Pengerang, the village of Kampong Pengelih and the town of Sungai Rengit.
Bumboats shuttle from Singapore's Changi Point Ferry Terminal to Pengerang from 7 AM in the morning to 7 PM in the evening, operating on a first-come-first-served basis: once 12 people show up, the boat leaves. The journey takes about an hour and costs S$9/person, plus S$2 for a bike. The last boats back leave by 4 PM.
If you miss the last bumboat, you can also take the Sebana Cove  ferry back to Singapore (4/5 services daily, last departure at 9 PM), but this is much more expensive (S$38 one-way) and you'll need to arrange a taxi to take you to Sebana Cove first.
Taxis shuttle between the Pengerang dock and Sungai Rengit for RM 6/person (shared) or RM 20/car (charter).
Bicycles can be rented in Sungai Rengit, or you can rent one at Changi and bring it with you.
Pengerang was the site of a major WW2-era British coastal battery. The part of it at Pengelih, right next to the immigration point, is open to the public but in a state of nature, with no trails, signs etc. Most of the rest is now used by the Malaysian military. 
Chinese pastries are a popular souvenir.
Seafood! It's the main reason to come here, with treats like lobster and crab much cheaper than Singapore or even JB.
There are three basic lodging places in town. If you want more luxury, head up the coast to Desaru's beach resorts.