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 Tanjung Pengelih, the village of Kampong Pengelih and the nearby town of Sungai Rengit.
Sungai Rengit is around 35 km south of Desaru, or 120 km from Johor Bahru. The distance from JB will decrease considerably once the Johor-Desaru Expressway opens. [Update] E22 is now open and the journey from JB to Desaru is now less than 1 hour.
By Bum boat
Take a bum boat from Changi Ferry Terminal towards Pengerang. Remember to go there early. Last bum boat is around 4pm++ SG time on weekend. It varies on weekday. There is no fix schedule so whenever it has 12 passengers or so then you are good to go. Price would be around SG$10-13 depending on number of passenger. Additional $2 for bike.
Taxis shuttle between the Pengerang dock and Sungai Rengit for RM 5/person (shared, four person minimum) 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.