Rotterdam's trams, buses and metro are very well arranged by the Rotterdam public transport organization RET. Most public transportation runs between 6am-12.30 in the night. There are night buses too like the Nachtnet and the BOB bus which use the same 14 lines to the outskirts of the city. The BOB bus runs on Friday & Saturday nights.
Tickets are sold by the bus driver (cash only!). Most night buses depart between 1am and 6am from Central Station. Check signs at the bus stops to find out which bus number you need to reach your destination. You can find RET information and service offices at the Rotterdam Central Station and Beurs. The smaller stations have machines where you can purchase tickets. On the bus you can also purchase a ticket from the driver and on trams there will be a conductor to sell you a ticket (cash only!).
The OV-chip card can be used on all metros (mandatory), trams and buses in Rotterdam. There are 3 kinds of OV-chip cards: personalized, anonymous & one time use. With the personalized card and the anonymous cards (which costs €7.50) you can upload the chip with money to take rides on public transportation in Rotterdam. When it starts to run low just load it up again. The benefit of the personalized card is that if you lose it you can report it at the RET office and block it so that no one else can use it. With the anonymous chip card you are also able to use it as many times as you need. The cost for traveling is € 0.75 to start + € 0.115 per kilometer. Then there are several types of disposable cards: 2 hours of travel (€ 3.50), 2 one way trips (€ 4.90) and day cards for 1(€ 6.-), 2 (€ 9.-) or 3 (€ 12.-) days of unlimited travel in metro/bus and tram. All types can be purchased at information and ticket offices at Metro stations: Central Station, Beurs, Zuidplein, Capelsebrug and Spijkenisse. The smaller metro stations only have machines where you can upload your card, purchase a ticket or just see how much credit is left on your card.
Rotterdam has a lot of water so why not use it for public transportation? There are different routes to take to visit different places not far from Rotterdam and you can take your bike with you for free!
Take the Waterbus for instance to Kinderdijk. The stop in Rotterdam is at the Willemskade (next to Spido under the Erasmus bridge). It departs here every half hour Mon-Fri from 7.00 am-8.00pm. In the weekend during summer (april-october) every half hour on Sat from 8.00am-9.00pm and Sun from 11.00am-7.30pm. During october-april in the weekend departures are every hour.
To get to the famous Dutch Windmills of Kinderdijk, change ferries at Ridderkerk De Schans for the "Driehoeksveer" ferry. To get here it takes 30 minutes from the Waterbus Rotterdam stop. Take the Waterbus from 10:30 in Rotterdam and there is a transfer every 30 minutes untill 5.00pm.
You can buy a HOP ON/ HOP OFF ticket at Waterbus which includes a transfer on the Driehoeksveer and entrance to the visiting windmill.
Right now it is messy at Rotterdam Central Station due to building and renovation work but trains still run frequently between main cities like Den Haag, Utrecht & Amsterdam or any other destination in the Netherlands. After 1am night trains run every hour between the major cities. Purchase your train ticket beforehand! You will receive a fine when you get caught without a ticket plus an extra surcharge for the ticket itself. Take intercity trains or the sneltrein (fast train) for major destinations. If you fancy a long journey or just want to visit a small city, the stoptrein stops at every single station. The ticket machines not only sell national tickets but also provide tickets for destinations in Belgium and Germany. For other international destinations you can best visit the international ticket counter located on the 1st floor of the blue building at the Station. Open Mon-Sat 7am-8.30pm, Sun 9am-8.30pm.