To travel with public transport in The Netherlands you need to purchase an OV-chip card (digital smartcard), on which put some money and use to check in before and out after traveling. Normally the cheapest option is to purchase an anonymous chip card. To purchase the City Card is only a better option if you plan to travel extensively within the city of Amsterdam.
Flying to Amsterdam is easiest to Amsterdam Schiphol International Airport. Transport into the city is best by train, which takes about 15 minutes and costs less than 5 euro (after buying a OV-chip card). It is not advisable to travel to Amsterdam by car, since parking downtown is difficult and expensive.
Amsterdam Central is also an international trainstation. Trains from Germany, Belgium and France arrive several times a day.
Is easiest by public transport, but Amsterdam is also famous for its bicycles. Distances are not too far and Amsterdam is relatively flat, so renting and driving a bike is an easy way to get around. For more information on travel and stay in Amsterdam, see this link