Well from Rotterdam to amsterdam central you'll need the train and that will take about 1 hour:
09:41 Rotterdam Centraal 8 Amsterdam Centraal Sneltrein (NS)
09:46 Schiedam Centrum
09:54 Delft
10:02 Den Haag HS
10:05 Den Haag Laan v NOI
10:14 Leiden Centraal
10:28 Heemstede-Aerdenhout
10:34 Haarlem
10:45 Amsterdam Sloterdijk
10:52 Amsterdam Centraal 1
cost € 24,30 return and 13,60 for a one-way!
You can get out at Amsterdam Sloterdijk and take tram 12 to Elizabeth wolfstraat or you can go from Amsterdam Centraal with tram 13 to Elizabeth wolfstraat. The tram will cost you about 1,80 one-way.
So It might be cheaper to fly to Schiphol?
You can get more info about trains in the Netherlands on
http://www.ns.nlOkay it's in Dutch, but I think it's easy to understand.
Check this for the cheapest stay in Amsterdam:
http://www.hostelsclub.com/