Getting from the airport (Schiphol) to your hotel
Schiphol is a transportation hub and therefore, there are trains to go to all parts of the Netherlands from here. There are trains that go to Amsterdam Central ~ every 15 minutes and a ticket costs ~€ 4.
Tickets can be purchased with credit card at the machines in Schiphol and Amsterdam Centraal ONLY; alternatively, tickets can be purchased at the counter (both charge a €,50 service charge).
These trains are operated by NS: http://www.ns.nl/en/travellers/home.
Check the schedule boards to determine what track your train is leaving from.
Getting around Amsterdam
Amsterdam is a very walkable city and is served by a convenient public transportation system operated by GVB: http://en.gvb.nl/pages/home.aspx.
I recommend purchasing a single day/multi-day pass, as one trip can cost you around € 2-3. Also, the passes are based on hours so if you activate a single day pass on Thursday at 4pm it is valid until Friday at 4pm.
For more information about pricing, visit this page: http://en.gvb.nl/ovinmamsterdam/Pages/bestdeal.aspx.
Maps are available at tourist information points; there is one in Schiphol and one opposite the Central Station.